EMIID)  WELOAMS  MEMORIAL 


<ub 


Preface  to  the  Second  Edition. 


The  student  will  find  this  to  be  no  entertaining  work 
of  literature,  but  a  lesson-book  for  instructive  and  thorough 
practice,  which  will  enable  him  to  gain  the  routine  indispen- 
sable in  our  art  and  for  our  time.  Misled  neither  by  the 
transient  successes  of  superficial  smartness,  nor  by  the  pre- 
tentiousness of  musical  cliques,  the  young  musician  should 
submit  himself  to  a  strict  course  of  training,  qualifying  him 
to  recognize  his  position  witii  respect  to  the  unceasing  develop- 
ment of  art. 

This  second  edition  has  benefitted  not  only  by  my  own 
uninteiTupted  work  as  a  teacher,  but  also  by  the  aid  of  the 
composer,  Mr.  Heinrich  Urban,  to  whom  my  best  thanks  are 
due  for  his  friendly  permission  to  use  his  notes. 

The  method  remains  unchanged  in  this  edition,  but  more 
attention  has,  in  general,  been  paid  to  the  preliminary  exer- 
cises. May  it  continue  to  further  the  cause  of  earnest  musical 
education! 

Ludwig  Bussler. 


3% 


Table  of  Contents. 


Page 

Preface Ill 

Introduction     •••• -..  1 

The  Science  of  Harmony. 

I.  On  the  Chords  of  the  Key. 
THE   PKINCIPAL    CHORDa 

A.  The  Consonant  Principal  Chords. 

§    1.    The  Tonic  Triad .    .    .    •  3 

§    2.    Triads  of  the  Dominant  and  Sub-dominant 4 

§    3.    Transposition.    Doubling , 5 

§    4.    Four-part  Chords 5 

§    5.    Interconnection  of  the  three  Fundamental  Triads  in  four- 
part  form *    .     .    .     .  6 

§    6.    Changed  position  of  higher  parts  in  the  Chord.    Exercise  1  7 

§    7.    Harmonizing  the  Scale.     False  progressions.     Exercise  2  9 

§    8.    Freer  use  of  the  three  Triads.    Exercise  3 13 

§    9.    Close  and  open  harmony ,    ...  16 

§  10.     Names,  compass,  and  treatment  of  the  parts 17 

§  11.    Treatment  of  open  harmony,  and  combination  of  both 

styles  of  harmony.    Exercise  4 18 

§  12.    Chord  of  the  Sixth.    Exercise  5 21 

§  13.    Chord  of  the  Fourth  and  Sixth.     Exercise  6          -    ...  23 

B.  The  Dissonant  Principal  Chords. 

§14.    Dominant  Chord  of  the  Seventh ,  29 

§  15.    Inversions  of  the  Dominant  Chord 30 

§  16.     Treatment  of  the  Dominant  Chord 31 

§  17.    Different  Styles  of  Close 32 


63Ci4:r 


—    VI    — 

Page 

§  18.    Dominant  Chord  of  the  Seventh,  and  Tonic  Chord  of  the 

Sixth  and  Fourth.     Exercise  7 .36 

§  19.    Chord  of  the  Ninth.     Exercise  8 39 

§  20.     Minor  and  Diminished  Chord  of  the  Seventh.     Exercise  9  44 

§  21.    The  Diminished  Triad.     Exercise  10 49 

§  22.    Freer  treatment  of  the  Chords.     Exercise  11  .    .    .    •    .  52 

THE    SUBORDINATE   CHORDS. 

§  23.     Major  and  Minor  Subordinate  Chords.     Exercise  12   •    ,  64 

§  24.     Inversions  of  Subordinate  Triads.     Exercise  13   ...    .  71 

§25.    Subordinate  Triad  on  the  second  degree  in  Major  and  Minor  73 

§26.     Subordinate  Triad  on  the  third  degree  in  Major.  Exercise  14  75 

§  27.  Other  free  leadings  of  the  Subordinate  Triads  ....  78 
§  28.     Subordinate    Chord     of    the    Seventh    on    the    second 

degree.    Exercise  15 ••••••  79 

THOROUGH-BASS   NOTATION. 

§  29.    Thorough-bass  Notation.    Exercise  16     •••••••  88 

II.  The  Tones  foreign  to  a  Harmony. 

§  30.    Introduction  .••••••«• 94 

PASSING-NOTES. 

§  31.    Simple  Passing-notes  in  one  part.     Exercise  17  ...    •  94 

§  32.     Simple  Passing-notes  in  several  parts.     Exercise  18    .     .  102 

§  33.    Complex  Passing-notes.     Exercise  19 105 

§  34.    Passing-notes    on    weak    beats.      Improper    Changing- 

notes.     Exercise  20 ••••••••.  107 

THE   SUSPENSIONS. 

§  35.    Tied  Suspensions  in  one  part.     Exercise  21,  22  .    .    .    ,  111 

§  36.    Tied  Suspensions  in  Bass.     Exercise  23 117 

§  37.    Tied  Suspensions  in  middle  parts.     Exercise  24     ,    .     .  118 

§  38.    Suspensions  in  two  parts.    Exercise  25 121 

§  39.  Retarded  Resolution  of  tied  Suspensions.  Exercise  26  .  122 
§  40.     Suspensions  from  below.  —  Suspensions  in  several  parts. 

Exercise  27 124 

§  41.    Free,  or  quite  unprepared,  Suspensions.    Exercise  28      .  128 

§  42.    Anticipation.    Exercise  29 130 

§  43.    Proper  Changing-notes 132 

§  44.    Free  treatment  of  foreign  tones,   and  combinations  of 

the  same.    Exercise  30 .,,»•..  133 


—  vn  — 

Page 

III.  Harmonic  Modulation. 

§  45.    The  Meaning  of  Modulation •    .  141 

§  46.    Change  of  Mode 142 

§  47.    Modulation  to  "Adjacent  Keys 144 

A.  The  Dissonant  Principal  Chords  as  a  means  of  modulation  from 

the  tonic  triad  of  a  key  to  that  of  any  other  key. 

§  48.    General  sketch  of  the  procedure 147 

§  49.    Cross-relation 148 

§  50.    Chord  of  the  Dominant  Seventh  in  Modulation.     Exer- 
cise 31,  32 150 

§  51.    Harmonic  Sequences.     Exercise  33 153 

§  52.    Modulatory  Phrases.    Exercise  34 157 

§  53.    Major  Chord  of  the  Ninth  in  Modulation.    Exercise  35  .  158 

§  54.    Minor  Chord  of  the  Seventh  in  Modulation.    Exercise  36  159 

§  65.     Minor  Chord  of  the  Ninth   in  Modulation.     Exercise  37  160 

§  56.    Diminished  Chord  of  the  Seventh.     Exercise  38,  39  .    .  161 
§  57.    Enharmonic  character  of  the  Diminished  Chord  of  the 

Seventh.     Exercise  40 166 

§  58.    The  Diminished  Triad.    Exercise  41 168 

§  59.     Substitutes  for  the  Sub -dominant  as  agents  in  Modu- 
lation.    Exercise  42,  43 168 

B.  Deceptive  Progressions. 

§  60.     Meaning  of  "Deceptive  Progression" 171 

§  61.    Deceptive  Progressions  of  the  Dominant  Chord.  Exercise  44  173 
§  62.     Deceptive  Progressions  of  the  Dominant  Triad  as  a  sub- 
stitute for  the  Dominant  Chord 174 

§  63.    Deceptive  Close 174 

§  64.     Deceptive  Progressions  of  the  other  Dissonant  Principal 

Chords.    Exercise  45 175 

§  65.    Sequences  with  Deceptive  Progressions.    Exercise  46      .  177 
§  66.    Deceptive  Progressions  of  the  Subordinate  Chord  of  the 

Seventh.    Exercise  47.  I 179 

§  67.    The  other  Subordinate  Chords  of  the  Seventh.  Exercise47.il  181 

C.  Progressions  of  Triads. 

§  68.    Progressions  of  Triads 183 

§  69.     Chord  -  Progression  and  Modulation  independent  of  the 

leading  of  the  parts  and  the  melody 184 

§  70.    Employment  of  Foreign  Tones  in  Modulation.   Exercise  48  187 


—  vm  — 

Pego 

IV.   The  Altered  or  Mixed  Chords. 

§  71.    Explanation  of  the  term 192 

§  72.    The  Subordinate  Triad  on  the  Flatted  Second.   Exercise  49  192 

§  73.    The  Augmented  Chord  of  the  Sixth.    Exercise  50      .    .  198 

§  74.    The  Augmented  Triad.    Exercise  51 205 

§  75.     Other  Mixed  Chords,  and  similar  Harmonies      ....  208 

§  76.    Organ-point.    Exercise  52 210 

§  77.     Modern  Closes 213 

§  78.     Thorough-bass  Notation.     Exercise  53 214 

§  79.    A  Master-work:  Ave  verum  corpus  by  Mozart.  Exercise  54  220 

Index ' 225 


■«»>■ 


Introduction. 


1.  The  Science  of  Harmony  forms  the  first  part,  and  the 
foundation,  of  the  art  of  composition,  because  in  it  the  funda- 
mental relations  of  the  Modes  find  their  simplest  and  fullest 
explanation.  It  has  for  its  subject  the  conditions  under  which 
tones  can  sound  together  and  progress  in  combination.  The 
connecting  principle,  in  harmonic  progressions,  being  the  Melody y 
the  chief  object  of  the  lessons  in  harmony  will  be  the  adding 
of  harmonies  to— harmonization  of— given  melodies. 

2.  The  rules  for  the  art  of  composition  are  indispensable 
aids  for  gaining  a  mastery  over  the  material  of  music;  but 
they  are  not  binding  laws  for  musical  art.  Therefore,  the 
finished  artist  (i.  e.:  one  who  is  equipped  with  all  the  resources 
of  his  art)  needs  these  rules  no  longer,  and  aesthetic  criticism 
has  no  right  to  hold  them  up  as  authoritative.  Decisive  for 
such  criticism  are,  rather,  the  laws  of  musical  art,  which  the 
artist  bears  in  his  consciousness,  and  whose  establishment  in 
plain  terms  is  the  task  of  the  science  of  music.  The  course 
in  composition  requires  the  peculiar  limitations  imposed  by 
these  rules;  partly  because  its  sphere  is  at  first  necessarily  a 
limited  one,  and  partly  to  prevent  the  student  from  losing  time 
in  following  wrong  paths. 

3.  The  exercises  in  the  harmony  lessons  are  based  upon 
the  requirements  of  the  four-part  vocal  chorus,  because  the 
conditions,  which  this  latter  imposes  upon  the  composer,  are 
the  best  preparatory  school  for  a  good  leading  of  the  parts. 

Bussler,  Elementary  Harmony.  1 


However,  some  of  the  exercises  liere  given  overstep  the  natural 
compass  of  the  voices,  because  the  science  of  harmony  under- 
takes the  thorough  ti-eatment  of  tonal  relations  which  pass 
beyond  vocal  limitations. 

4.  The  Exercises  and  Model  Examples,  arranged  for  teach- 
ing special  points,  must,  of  course,  not  be  judged  from  a  purely 
aesthetic  standpoint,  but  as  parts  of  a  methodic  whole.  Still, 
they  have,  besides  their  importance  for  the  several  exercises, 
this  great  advantage:  That  they  plainly  mark  out  the  degree 
of  skill  to  be  attained  through  the  exclusive  study  of  the 
science  of  harmony. 

5.  The  limit  of  the  lessons  in  harmony  is  fixed  by  their 
relation  to  the  whole  art  of  composition,  and  to  the  practical 
needs  of  the  course  of  study.  Respecting  this  latter,  a  course 
in  a  public  institution,  i.  e.:  class-instruction,  is  here  kept  in 
view,  such  a  course  including  the  conditions  of  the  others. 
The  teacher  must  be  free  to  fix  the  length  of  the  course,  this 
naturally  depending  upon  the  special  aims  of  the  instruction, 
and  the  abilities  of  the  pupils. 

6.  As  a  preparation  for  the  study  of  Harmony,  thorough 
familiarity  with  the  rudiments  of  music,  and  a  certain  skill  in 
playing  or  singing,  are  required. 

REMARK.  The  Science  of  Harmony  in  its  present  form 
was  created  by  J.  B.  Rameau,  (d.  1764  in  Paris).  During  its 
existence  of  150  years  it  has  attracted  the  attention  of  emi- 
nent minds,  and  its  development  has,  consequently,  been  rapid 
and  fulL 


The  Science  of  Harmony. 

I.  On  the  Chords  of  the  Key. 

The  Principal  Chords. 
A.  The  Consonant  Principal  Chords. 

§1. 

THE  TONIC  TRIAD. 

The  tonic,  the  third,  and  the  fifth  of  the  key  form,  when 
oombinedj  the  tonic  triad, 

C-major. 


i 


^ 6^—^^-^- 


^=^=.2=-: 


No.  1. 

C-minor.* 


I 


Et2==zzzz=£i^Efe: 


The  tonic  triad  should  first  be  sung,  then  played  on 
the  piano  or  harmonium,**  and  finally  written  out,***  in  all 
major  and  minor  keys. 

*  The  course  in  harmony  is  founded  on  the  harmonic  minor  scale. 
**  For  a  harmony  course  the  harmonium  is  preferable  to  the  piano,  be- 
cause each  part  is  fully  sustained,  especially  in  suspensions.     It  is  highly  ad- 
vantageous to  employ  both  instruments. 

***  These  three  methods  of  exhibition  should  be  applied  to  all  similar 
exercises  following. 

1* 


—     4     — 

The  intervals  of  all  chords  are  calculated  from  the  loivest 
tone  in  the  same.  Consequently,  the  tonic  triad  in  major  has 
a  major  third,  and  in  minor  a  minor  third;  both  have  a  per- 
fect fifth. 

Every  triad  with  major  third  and  perfect  fifth  is  called 
a  major  triad.  Every  triad  with  minor  third  and  perfect  fifth 
is  called  a  minor  triad.  In  a  major  triad  the  third  forms  with 
the  fifth  a  minor  third;  in  a  minor  triad  a  major  third. 


§2. 

TRIADS  OF  THE  DOMINANT  AND  SUB-DOMINANT. 

If  a  triad  be  constructed  on  the  fourth  degree  of  the  key, 
it  forms 

in  major  a  major  triad, 
in  minor  a  minor  triad. 


I 


-?5r 


.-^=:fcz^ 


6» «2. 


t^ 


%—^-=i 


The  fourth  degree  being  called,  in  its  relation  to  the  key, 
the  sub-dominant,  this  ti-iad  is  called  the  sub-dominant  triad, 

Fopm  this  triad  in  all  major  and  minop  keys. 

If  a  ti'iad  be  erected  on  the  fifth  degree,  a  major  triad 
results  both  in  major  and  minor. 


i 


I 


i 


W- 


ir 


-^ 


1^^ 


The  fifth  being  called  the  dominant,  this  triad  is  called 
the  dominant  triad. 

Form   the   same   in  all   major  and   minor  keys.     All   three 

fundamental  triads  in  like  manner. 


—     5 


In  writing,  chords  are  indicated  by  Roman  numerals  cor- 
responding to  the  degree  of  their  tonic;  thus,  the  tonic  triad 
by  I,  the  sub-dominant  triad  by  IV,  the  dominant  triad  by  V. 


§  3. 
TRANSPOSITION. 


DOUBLING. 


The  name  of  a  chord  is  unchanged  by  a  transposition 
of  its  higher  tones  (parts),  as  long  as  the  bass  or  lowest  tone 
remains  the  same: 


4 


±^- 


and  also  when,  under  like  conditions,  any  tones  of  the  chord 
are  repeated  in  higher  octaves,  i.  Qr,  doubled. 


pi 


■gr 


5 


Form  triads  with  various  positions  of  the  higher  parts, 
and  also  with  doublings  of  the  parts. 

§4. 
FOUR-PART   CHORDS. 

Triads  are  changed  to  four-part  chords  by  doubling  one  tone. 

RULE,  hi  four-part  music  the  doubling  of  the  third 
should  generally  be  avoided. 

In  a  four-part  chord  either  the  octave  (of  the  tonic),  the 
third,  or  the  fifth,  may  be  in  the  highest  part. 


* 


zsr. 


Construct  triads  In  four- part  form. 


—     6     — 


§5. 

INTERCONNECTION  OF  THE  THREE  FUNDAMENTAL 
TRIADS  IN  FOUR-PART  FORM. 

As   the   connectiug   link,   in   tlie  succession  of  the  three 
fundamental  triads,  we  find 

the  common  tone  in  tlie  same  part. 

Interconnection  of  chords. 


7.     C-major. 


m 


C-minor. 


.%=&=f^ 


££ 


a^Pl 


:g==2=:gs22g;^Eg 


EE 


3?: 


i?i 


11 


lY 


I       IV 


^g— ^— ^ — g— ^- 

-i^u-9.-^—9^.-^f,—9^-\ 

-^ — ^ ^ 14 

J         <>      •               <>                     rj 

-V-\y-^ '-' ''-A\ 

I       IV       I 


IV       I 


In  this  exami3le  the  inner  parts  are  kept   as  close   as   pos- 
sible  to   the   highest   part,  thus   forming   close   harmony.     The 
•bass   approaches   or    retreats    from    the    higher   parts    at    will. 
For  the  leading  of   the  bass   observe  the   following   directions  : 
Avoid  skips  more  extended  than  an  octave. 


8. 


Bad. 


I 


Si 


Avoid  the  succession  of  two  fifths  or  two  fourths  in  the 

same  direction,  (motion), 

9. 


g 


;=3 


Bad. 


Fifth     Fifth     Fifth     Fifth 


l^^l 


Bad. 


Fourth    Fourth    Fourth    Fourth 


But  good: 
10. 


^=1^: 


%-=^-=.^. 


9= 


Fifth      Fourth       Fifth      Fourth 


Play  at  the  Instrument,  in  like  manner,  the  chord -pro- 
gressions l-IV-l-V-l  in  all  keys;  I.  with  octave  as  highest 
tone,  2.  with  third,  3.  with  fifth,  as  shown  in  No.  7. 


§6. 

CHANGED  POSITION  OF  HIGHER  PARTS  IN  THE  CHORD. 

Where  the  melody  employs  in  succession  the  tones  of  a  chord 
the  inner  parts  systematically  follow  it. 

j         J 

1 1 \ G Tl 


11. 


I 


r 


f=f 


p 


^=t 


:g=--g 


Here  all  tones  of  the  higher  parts   are   found  together, 
but  never  in  the  same  part. 

Proceed   as   above   in   the   following   Exercises;    but,    in 

progressions   between   different  chords,  the   common  tone  must 
be  sustained  in  the  same  part,  as  directed  in  the  foregoing  section. 


—     8     — 

Exercise  1. 

To  harmonize,  In  four  parts,  given  melodies  In  major 
and  minor,  with  the  three  triads. 

In  these  exercises,  each  tone  of  the  melody  takes  one  of 
the  three  fundamental  triads.  First  write  out  the  bass  to  the 
entire  melody,  then  add  the  inner  parts  as  close  as  possible 
to  the  given  highest  part.  The  bass  is  to  be  written  according 
to  directions  found  in  the  foregoing  section. 


Andante, 


Model  1. 


^# 


^=J=^ds=ri 


*n=^^^s* 


U 


£5 


3 


^jv'-i-ri] 


Here  the  monotony  of  the  bass  is  partly  relieved  by 
taking  the  few  tones  at  our  disposal  in  different  octaves.  The 
following  examples  for  practice  are,  like  the  model,  to  be 
worked  out  on  two  staves  with  violin  and  bass-clefs. 


Elxamples  for  Practice. 


x-V 


^^^^^^ 


1 


MSi^^^ipi:^^^ 


^psa^ 


±=A 


^?zl=t 


-z?- 


3ES 


^M^ 


—      9      -^ 


The  style  of  notation  should  follow  the  model.  For  this 
reason  the  stems  in  the  soprano  are  turned  up,  and  the  inner  parts 
turned  down.     In  later  examples  this  will  be  left  to  the  pupil. 

§  7. 
HARMONIZING  THE  SCALE.     FALSE  PROGRESSIONS. 

As  soprano,  the  ascending  and  descending  major  scale  is 
given,  and  is  to  be  harmonized  in  four  parts  with  the  three 
fundamental  triads.  The  two  inner  parts  are  to  be  placed  as 
close  as  possible  to  the  soprano. 

First,  we  will  place  the  tonic  triad  to  all  tones  which  belong 
to  it ;  i.  e,  :  to  the  prime,  third,  fifth,  and  octave  of  the  scale. 
12. 


m 


m 


^^d 


i 


s 


-«5»- 


2^ 


m 


tp* 


i 


^^=^ 


^- 


stz?^: 


f 


i^ 


Now,  those  remaining  tones  of  the  scale  which  belong  to  the 
sub-dominant  triad,  i.  e,:the  fourth  and  the  sixth,  take  this  chord. 


rli     ,1 — 1+1—^4 

-J-^  4-Jr-  ^^-  -1— f  ^r— 

^  f=    --f  1  1*^  1 — I- 

fj    K>          1      «>  1 1      jv          r^ 

Finally,  the  second  and  seventh  take  the  dominant  triad, 
to  which  they  belong. 


^^^^^^ 


f 


=1: 


IWI 


3ja 


n 


T  I 


1 


^ 


^ 


^ 


^ 


^ 


10    — 


The  example  as  finislied  shows,  where  the  melody  pro- 
gresses from  the  sixth  to  the  seventh  degree,  three  faults. 

First,  while  elsewhere,  between  two  consecutive  chords, 
a  tone  common  to  both  is  found, 


15. 


I 


:g2s: 


-tr 


-TT- 


g: 


7g- 


no  such  common  tone  connects  the  chords  on  the  sixth  and 
seventh  degrees  of  the  scale. 


16.  <^ 


P 


^=^-- 


RULE.      Two  parts    must   not  ])rogress    in  perfect  fifths 
in     succession   in  j9«r«//e?  7notion. 

Secondly  J  the  third  part  (counting  from  above*)  progi-esses 


with  the  bass  in  parallel  fifths    9i:zfz^t=  »    *^^*  ^^i    ^^*^ 

parts,  while  progressing  in  the  same  direction^parallel  motion — 
form  the  interval  of  a  perfect  fifth  in  both  chords. 

RULE.     Two  parts   must  not  progress  in  perfect  fiftlis 
in  succession  in  parallel  motion. 

Consequently,  all  the  following  progressions  are  faulty: 
17.  _ 


-7^ 


-o- 


-&~ 


^^J.SS^ 


9fc 


42aL 


-<9-^ja- 


*  Comp.,  by  the  same  author,  Elements  of  Harmony  and  Notation, 
with  58  Exercises,  New  York,  G.  Schirmer. 


—   11   — 

Thirdly,  the  second  and  tSra  parts  progress  in  parallel 
octaves;  that  is,  both  parts,  while  progressing  in  parallel 
motion,  form  the  interval  of  an  octave  in  both  chords. 


18. 


I 


9i=- 


R  TILE.  Two  parts  must  not  progress  in  parallel  octaves 
in  succession.  Consequently,  the  following  chord-progressions 
are  faulty  : 


19. 


-^^ 


^^^^ 


-d. 


In  the  descending  scale,  the  same  three  faults  are  observ- 
able between  the  seventh  and  sixth  degrees; 


20. 


^^^ 


■r 


75'- 


.^=1 


that  is,  the  want  of  common  tones,  the  parallel  fifths,  and  the 
parallel  octaves. 

The  same  faults  appear  in  the  same  places,   when  the 
minor  scale  is  harmonized  according  to  this  plan. 
21. 


—     12 


To  avoid  these  mistakes,  we  will  abstain,  in  the  next- 
following  examples  for  practice,  from  taking  the  step  from  the 
sixth  to  the  seventh  degi-ee  in  ascending,  and  from  the  seventh 
to  the  sixth  degree  in  descending  progression. 


22. 


5^ 


=^^I: 


\ 


"^ 


g  />  <>> 


© 


-O- 


» o z> =" — 

Here,  in  contradistinction  to  No.  7  and  11,  the  common 
tone  passes,  even  in  successions  of  diiferent  chords,  from  one 
part  to  another. 

Exercise  2. 
Harmonize  the  following  melodies  according  to  method 

shown  In  above  scale. 

Model  2. 


i 


f 


# 


rf  rr-r 


93 


E 


& 


I 


51=3 


^^ 


# 


f  fTf  f  f 


^ 


? 


^ 


s; 


e 


->5>- 


I 


5. 


^ 


^ 


Examples  for  Practice. 

1^ 


l9=^-"- 


eS^ 


|6^ 


31 


#^^ 


3 


^ 


—     13 


:i; 


#-»-!* 


=^Eg=B 


?='=f 


3^= 


#— ^ 


iiSi^H 


iia-*f 


ti5t=t: 


t^pti 


f^f=?3^ 


s 


■•-* 


33 


yfe^ 


EEE'tE?^ 


feEl^l^:^ 


-^— r^ 


iS 


-#— # 


^^S 


§8. 

FREER  USE  OF  THE  THREE  TRIADS. 

While  each  other  degree  of  the  scale  belongs  to  but  one 
fundamental  triad,  the  fifth  is  common  to  both  the  tonic  and 
the  dominant  triads,  and  the  tonic  (octave)  to  both  the  tonic 
and  sub-dominant  triads  (§  5). 

23. 


i 


m 


is: 


-0- 


'W 


t^. 


W 


-^ 


^'Mrri?-^- 


-/2- 


fini^s: 


Therefore,  wherever  the  tonic  or  the  fifth  appears  in  a 
melody,  we  have  the  choice  between  two  triads. 

Hitherto,  we  have  avoided  the  progression  IV — V  (sub- 
dominant  triad  to  dominant)  because  no  common  tone  is  pre- 
sent.    This  progression^  is  nevertheless,  allowable,  when 

1.  The  bass  progresses  by  a  step; 

2.  The  higher  parts  progress  in  a  contrary  direction — in 
contrary  motion— to  the  bass; 

3.  These  two  chords  are  followed  by  the  tonic  triad. 
Under  these  conditions,  IV — V — I  is,  therefore,  allowed. 
But  the  reverse  progression  V — IV — I  is  not  allowed. 


14     — 


24.    Good. 


^^^ffl^i^^ffi 


\i-^ 


:^=2 


31: 


22: 


Ff 


is::: 


IV  V  I 

The  above  succession  of  chords  forms  a  suitable  dose 
(cadence)j  which  we  can  consti'uct  from  our  first  examples  of 
chord-connection  (No.  7)  by  omitting  the  third  chord. 


^^Pi 


ig: 


^ 


W 


^=Si 


'^~W 


1 


ISl 


-zr. 


-^^=^ 


25. 


zua 


^m. 


-Cd- 


g: 


ii3l; 


s 


^^^ 


W 


«9 


zzs: 


szzzz 


-Z? 6> 


Form  this  close  in  all  major  and  minor  keys,  at  the  in- 
strument 

The  bass  may  form  as  wide  an  interval  as  desired  with 
the  other  parts,  and  approach  them  as  far  as  unison  with  the 
third  part.  But,  the  unison  must  proceed  from  contrary  or 
oblique  motion  (where  one  part  moves  while  the  other  is 
stationary);  two  parts  must  never  progress  together  in  unison. 


26. 


^#=3= 


-W~^ 


^»=t 


m^ 


Wrong  progressions  can  be  avoided  by  contrary  motion. 


—     15     — 

Bass-skips  of  a  seventh  are  forbidden.  A  repeated  chord 
Is  equal  harmonically  to  the  same  chord.  For  a  change  of 
chords  the  strong  beat  is  preferable. 

Exercise  3. 

Harmonize   melodies  with  four  parts,  with  the  three 

fundamental  triads,   according  to  directions  given   in  this 

section. 

Model  3. 


IV  V  I 

Examples  for  Practice. 


10. 


i 


^^g=p 


11. 


^n=fv^^ 


ti=t=^=\ 


'  r   r    ' 


i 


^^^^^m\ 


^=a 


fczt 


-W—^ 


12. 


e 


^Ef 


^Ji=F 


:t=t: 


^=^1 


13: 


-     16     — 


:iJ 


r^ 


^^^^EJEpj-^^^a^BJE^ 


15. 


fflbf=f=?t^=r=gfeEgffa^gp5g 


m 


-|i->-4- 


t=t 


I^ZZ^ 


1^1=:^ 


^  16: 

P 


E^JBE^tt 


•    d    • 


i 


I 


17. 


J— ^4-<9-i*, 


£S3^ 


t^h 


^ 


S 


<g— ^ 


■^ 


§9. 

CLOSE  AND  OPEN  HARMONY. 

When  two  parts,  in  a  chord,  lie  so  near  to2:ether  that  no 

tone   of   the   same    chord    can   be   placed   between   them,   they 
are  said  to  be  in  close  position ;  e.  g.  :  the  two  higher  parts  in 


this    chord  :      'v?)~~^f~~     because    no   tone   belonging  to   the 
chord  c — e — g  can  be  placed  between  them  ;    or  here  the  three 

n j2 

lower  parts  :     t~ 


t 


On  the   other   hand,  when  a  tone  of   the   same    chord  can 
be  23laced  between  two    adjacent    parts,  they  are   in   ope7i  ^Josi- 

tioii ;  e.  g.  :  these  three  higher  parts  :    'jm—^^^~—^  i  because  the 

black    notes   g   and    c,  belonging    to    the    same   chord,  can   be 
placed  between  them. 


—     17     — 

In  former  exercises  we  have  placed  the  inner  parts  in  such 
a  manner  as-  to  form  close  harmony  with  each  other  and  with 
the  soprano.  That  form  of  a  chord,  in  which  the  three  highest 
parts  lie  together  in  close  position,   is  called  close  harmony. 

Under  open  harmony  is  understood,  in  opposition  to  close 
harmony,  that  form  of  a  chord  in  which  the  three  highest 
parts  are  spread  over  the  compass  of  an  octave  or  more. 


Close. 


27. 


fe 


Open. 


;i 


.a „ 


is: 


g: 


^ 


Form  triads  in  open  harmony  at  the  instrument. 


§  1<^- 
NAMES,  COMPASS,  AND  TREATMENT  OF  THE  PARTS. 

In  our  four-part  exercises  we  name  (after  the  four  chief 
varieties  of  the  human  voice),  tlie  first  part  the  Soprano;  the 
second,  the  Alto  ;  the  third,  the  Tenor ;  the  fourth,  the  Bass. 
These  four  parts  we  shall  consider  as  the  instrument  for  exe- 
cuting our  exercises,  and  confine,  for  the  present,  the  compass  of 


the  soprano  from 


of  the  tenor  from 


to: 


,  of  the  alto  from 


-^- 


9^ 


?zto: 


,  exactly  an  octave  lower  than 


the  soprano,  and  of  the  bass  from  ^i tozzzz:  * 


The  highest  and  lowest  tones  of  a  part  must  not  succeed 
each  other  at  short  intervals. 

The  lower  the  parts  on  the  whole  lie,  the  more  care 
should  be  taken  to  avoid  crowding  them  below. 


*  An  example  of  closest  harmony,  because  the  middle  parts  lie 
as  close  as  possible  to  both  outer  parts. 
B ussier.  Elementary  Harmony. 


—     18     — 

To  facilitate  the  leading  of  the  parts,  or  to  carry  out 
harmonization  in  any  desired  position,  one  tone  of  a  chord 
may  occasionally  be  omitted,  and  another  doubled  to  take 
its  place.     In  such  a  case,  UHads  omit  the  fifth. 

§11. 
TREATMENT    OF    OPEN   HARMONY,    AND    COMBINA- 
TION OF  BOTH   STYLES  OF  HARMONY. 

This  new  method  of  harmonization  is  specially  advantageous 
for  the  inner  parts,  which  no  longer  need  follow  the  progression 
of  the  soprano. 

However,  the  greater  freedom  thus  attained  renders  it 
necessary  to  consider  the  general  laws  for  the  leading  of  the 
parts,  in  so  far  as  our  present  purpose  requires. 

I.  The  chief  faults,  in  leading  the  parts,  spring  from  pro- 
gression in  like  direction,  technically  termed 

parallel  motion, 

and  may  be  avoided  by  leading  in  a  contrary  direction,    or 

contrary  motion.  But  contrary  motion  should  never  be  employed 

at  the  expense  of  a  good  leading  of  any  part  (e.  g.;a  bass- 

^_^kip  or  a  seventh). 

1  Write  out  in  some  keys,   and  play  in  all,  the  chord- 

progressions  I— IV— I— V— I  (§  5,  No.  7),  in  open  harmony. 

In  harmonizing  the  scale,  all  mistakes  between  the  6^^ 
and  7^^  degrees  may  be  avoided  by  changing  from  close  to 
open  harmony,  thus: 


28. 


f\ 

\j 

V^y        iCt 

-Gh 

-^rj        ^ 

c|:      G 

aQ     -^ 

^- 

^ 

or 


close  open  open  close  open  open 

The  reverse  progression  7 — 6  cannot  as  yet  be  achieved 
through  open  harmony,  because  its  faultiness  resides  in  the 
succession  V— IV  itself,   and  not  in  the  leading  of  the  parts. 


^      19      — 

II.  Of  the  three  highest  parts,  no  two  should  ever  extend 
farther  apart  than  an  octave.  The  bass  may,  as  we  know,  retreat 
at  pleasure  from  the  other  parts,  or  approach  them  up  to 
unison  with  the  tenor.  Two  higher  parts  may  also  join  to 
form  a   unison,    but   must    never   progress   together   in   unison. 

III.  In  the  leading  of  the  inner  parts  a  tone  common 
to  two  chords  should,  where  possible,  be  retained  in  the  same 
part.  Open  harmony  often  renders  this  possible,  where  an  ex- 
clusive use  of  close  harmony  would  prevent  it.     E.  g. : 


29. 


?^3= 


Open  posi- 
tion of 


the  first  I       _^ 


§i=s 


■^ chord  better:      — — (2- 

t=  ^ 1- 


Progression  by  degrees  is  preferable;  more  especia"  .  '?k 
to    avoid    simultaneous   skips   in  all   four    parts  ;  thou   '  h 

progressions  are  occasionally  employed  by  composers  '  «  ^  can 
related  chords  (i.  e. :  chords  possessing  tones  in  common  :.  r. :  ips 
are  allowable  where  a  chord  is  repeated  ;  diminished  and 
augmented  intervals  should  be  avoided,  where  possible,  in 
the  inner  parts  and  bass.  When  unavoidable,  the  diminished 
are  to  be  preferred. 

Octave  skips  are  permissible  in  progressions  between  dif- 
ferent chords,  but  can  rarely  be  employed.  Skips  of  a  seventh 
are  not  allowed  ;  major  sixths  in  ascending  are  only  allowable 
when  the  leading  of  the  part  is  otherwise  favorable  ;  in  de- 
scending, avoid  major  and  minor  sixths.  In  the  inner  parts, 
as  in  the  bass,  two  skips  of  a  fourth  or  a  fifth  in  the  same 
direction,  either  ascending  or  descending,  are  not  allowed  ; 
this  is  binding  for  any  two  more  extended  skips. 

An  unmelodic  leading  of  the  parts  is  most  easily  recog- 
nized by  singing  each  part  separately. 

2* 


—     20 


Exercise  4. 

Harmonization  of  Melodies  in  Open  Harmony. 

Model  4. 


I 


5 


^^ 


5 


^ 


&- 


^^ 


e 


f=f 


f=F 


(g    o- 


r 


^ 


^Jh^-J-^ 


^-^ 


:^z:±=: 


f   f  r '  r  r  r '  r  r=r 


d     d    d 


JA^^^ 


rrr 


p 


-g    (g 


S 


f=F 


f 


^- 


r 


r 


1.  The  first  three  chords  are  written  in  close  harmony  ;  for, 
otherwise^  it  would  be  necessary  either  to  place  the  lowest  parts 
very  low  and  close,  or  to  write  a  unison  on  the  second 
quarter-note. 

2.  Here  it  was  necessary  to  choose  close  position,  because 
f  in  the  tenor  would  have  caused  either  parallel  fifths  or 
a.  unison    in  the   following  chord. 

3.  Here  the  fifth  is  omitted  in  favor  of  more  open  har- 
mony. 

•i.  The  leading  of  the  parts  requires  close  harmony  here. 
It  is  plain,  that  open  harmony  cannot  be  exclusively  employed. 


21     — 


but   alternates   with   close  harmony  as  euphony  and  a  good 
leading  may  require. 

Examples  for  practice,  Nos.  1,  2,  3,  10,  11,  12,  13  and  14, 
may  be  used  as  exercises.  ^       ~ 

§  12. 

CHORD  OF  THE  SIXTH. 

By  changing  the  relative  position  of  the  tones  of  a  triad,  so 
that  the  third  is  chosen  as  Bass,  we  obtain  the  first  inversio7i  of 
the  triad,  the  Chord  of  the  Sixth, 


^- 


JSL. 


S 


I?^- 


-<@ <©- 


^ 


9£ 


-^- 


K 


t={: 


or  in*  full,  chord  of  the  third  and  sixth,  from  the  intervals 
which  its  higher  parts  form  with  the  bass.  But  it  is  always 
known  by  the  first  name.  The  chord  of  the  sixth  derived  from 
the  major  triad  has  a  minor  third  and  minor  sixth;  that  of 
the  minor  triad  has  a  major  third  and  major  sixth. 

The  bass-note  of  this  chord,  being  the  third  in  the  fun- 
damental choi'd,  should  not  be  doubled.    (Comp.  §  4,  Rule). 

Form  foup-part  chords  of  the  sixth  from  triads  of  all 
keys. 

The  chord  of  the  sixth  may  everywhere  be  substituted 
for  the  fundamental  chord,  except  in  the  close  and  (for  the 
present)  at  the  beginning. 

Like  every  newly-learned  chord,  the  chord  of  the  sixth 
facilitates  a  good  leading.  Contrarily,  the  persistent  employ- 
ment of  one  style  of  harmony  (either  open  or  close)  becomes 
more  difficult. 

For  variety  in  harmonization,  and  in  the  melody  of  the 
bass,  the  chord  of  the  sixth  may  be  used  advantageously  in 
alternation  with  the  fundamental  chord. 


—     22     — 


I 


31. 


% 


-Xli 


-Ci- 


I       6        V       e         I       < 

Similarly  in  minor. 

Two  successive  chords  of  the  sixth,  esi^ecially  in  major, 
and  progressing  as  shown  in  Ex.  32,  «,  are  in  vogue  among  com- 
posers. 

,      a    .  II  ,         . 


32. 


3 


-/^ 


\ 

I       ! 


<9 — >^v— ] 


6  6 

Three  successive  chords  of  the  sixth  are  seldom  of  good  effect. 


I^ 


-&- 


G- 


G- 


5t 


-?y- 


# 


3i 


1^ 


As  compared  with  the  fundamental  chord,  the  inversion 
secures  greater  ease  and  fluency  of  progression,  particularly 
in  the  melodic  leading  of  the  bass.  But  if  the  same  inversion 
be  persistently  employed,  this  advantage  is  lost,  and  the  bass 
progresses  by  extended  skips,  as  before. 

The  following  examples  show  the  advantages  of  using 
chords  of  the  sixth  when  a  melody-note  is  repeated. 


34. 


3 


i^ 


1^ 


-^ 


-?5'- 


^ 


1 


9^^=^=^-^ 


i 


-\ — 


IV 


—V   23 


Exercise  6. 

Write  out  the  following  examples  for  practice  in  four 
parts,  using  the  chord  of  the  sixth. 

Model  5. 


I 


i 


s 


fTffr^rf=f=F^ 


jjjjjj^ 


iii^  J.1 


-^ 


*3 


Wf 


^— # 


f 


f^ 


Examples  for  Practice. 


r£^^ 


^T-» 


Ea 


!«— 6» 


-I — r 


^S: 


:t=±=t 


i^t2=:t=t 


i^ 


19. 


l=lE3 


*=t: 


g^^E^':^ 


u 


p^ 


S3HEf 


lilg 


=Mf 


.<5»- 


I 


'20. 


i^^^-.3Ei^;?^^EEi 


1^ 


1^^ 


t-iy^ 


^  All  former  examples  may  be  used  as  exercises. 

§  13. 

CHORD  OF  THE  FOURTH  AND  SIXTH. 

By  using  the  ffth  of  the  triad  as  bass-note,  we  obtain 
the  second  inversion  of  the  triad,  called  the  chord  of  the 
fourth  and  sixth  from  the  intervals  formed  by  its  higher  notes 
with  the  bass. 


24     — 


35. 


The  chord  of  the  fourth  and  sixth  derived  from  the  major 
triad  has  a  perfect  fourth  and  major  sixth;  that  of  the  minor 
triad  has  a  perfect  fourth  and  minor  sixth. 

The  rule,  that  the  third  of  the  triad  must  not  be  doubled, 
likewise  holds  good  for  the  stxth  of  this  chord,  which  was 
the  third  of  the  fundamental  chord. 

Form  four-part  chords  of  the  foupth-and-sixth  of  triads 
in  ail  keys. 

The  employment  of  the  chord  of  the  fourth  and  sixth  is 
dependent  upon  various  conditions.  It  is  even  less  adapted 
for  a  beginning  or  closing  chord  than  the  chord  of  the  sixth. 

At  first  we  shall  use  it  only  in  the  following  cases: 

1.  When  the  chord  of  the  fourth  and  sixth  is  resolved  to 
the  triad  on  the  same  bass-note;  the  chord  of  the  fourth  and 
sixth  occupying  a  (relatively)  strong  beat;  and  both  fourth  and 
sixth  descending  in  degreewise  progression. 


36. 


I 


:» 


(^ 


-\ — r 


mi 


r=^ 


t=t 


t=^- 


I      I 


i 


2.  When  three  successive  tones  in  the  bass  progress  by 
degrees,  the  middle  tone  may  take  a  chord  of  the  J,  whose 
fourth  and  sixth  are  not  obliged  to  progress  by  steps.  Beat 
indifferent. 


37. 


—     25 


3.  With  three  similar  bass-notes,  the  chord  of  the  |  is  placed 
over  the  second  note,  and  fourth-and-sixth  progress  by  degrees. 
Beat  indifferent. 


~M-    -&    ^ 
I       I       I 


ip 


JzzjziibJ 


% 


121 


^ 


-^- 


r 


-^     -ri- 


1 \—X 


-^ 


t=\-=x 


A  five-chord  cadence  results  from  the  succession  of  chords 
in  §  5,  No.  7,  if  we  substitute,  for  the  tonic  triad  holding  the 
third  place,  its  second  inversion  (chord  of  the  4): 


89. 


P 


\ ^- 


-j^ 


^^^ 


r 


.Oi- 


^^l^i^l^si: 


-«r 


Play  this  cadence  in  all  keys. 

This  contains  the  chords  of  the  fourth  and  sixth  in  its 
by  far  the  most  usual  application,  its  employment  being  other- 
wise uncommon  and  restricted. 

In  freer  variations: 

-A- 


40. 


^ 


t-^-r- 


-g — <9- 


=g= 


-#-^-^- 


-25*- 


f 


_^_ 


-&—G- 


m 


Jill 


^^ 


-f^- 


i 
With  chord  of  the  sixth  derived  from  sub-dominant: 


41. 


fii^ 


a- 


-&- 


&- 


w^t 


r-tzz 


I — r 
.(St — ^ 


-&-^ 


i^ 


—     26     — 

The  melody  sometimes  occasions  a  variation,  as  compared 
with  directions  given  under  1,  from  the  degreewise  progression 
of   the   fourth-and-sixth   downward  ;   as  in  the  following  cases: 


42. 


^^ 


i--Tt 


(i)  I 


^g 


As  the  chord  of  the  I  must  always  fall,  in  this  cadence, 
upon  a  relatively  strong  beat  as  compared  with  the  dominant 
triad  which  succeeds  it,  it  should  be  observed^  that  in  triple 
time,  or  in  triple  subdivisions  of  measure,  the  second  beat  is 
held  to  be  stronger  than  the  third,  harmonically  considered.* 

S.  =  strong,  w.  =  weak. 


y^^ieii^^^™^ 


*  The  reason  of  this  is  given  in  the  science  of  music,  which  latter 
is  no  field  for  students  of  composition,  Hauptmann  explains  the  matter 
from  his  standpoint  in  "Harmonik  und  Metrik". 


'^^^^^^ 


1  Play  at  the  instrument  similar  cadences  in  major  and 

\    ininor  keys. 

The  use  of  both  inversions  admits  of  certain  variations 
in  the  ascending  scale, 


U. 


usual : 


(9—^ 


G ^ 


-j^3 f9 " ^« -^^ 


^-^-z. 


TC 19- 


I 


m 


& -G- 


-&- 


G c^ 


6  6 


45. 


uncommon: 


% 


— ryzy—o- 


-6-— g— &— g:::^g=| 


511^ 


-^ ^ 6»- 


«     ! 


p 


(6'-major  is  chosen  as  better  suited  to  range  of  voices) 
at  present  these  offer  no  particular  advantages. 

The  gain  is  greater  in  the  case  of  repeated  tones. 

^-r— J- 


75^—:^ 


-?5'- 


11 


t=X- 


r=^- 


1=? 


m 


46. 


5£i 


I  r 

1     I 


-%^±=^=:^- 


T  ' 


g 


I    I 


vs*- 


g^    g/- 


-^- 


^ 


:^ 


^s*— <>- 


I 


Form  similar  chord-successions  at  the  instrument. 


Exercise  6. 

To  harmonize  melodies  in  four  parts,  using  the  three 
triads  and  their  inversions  in  close  and  open  harmony. 


Model  6. 


I 


I 


Cl( 


U=i 


i 


fTTTf 


s:^ 


e 


t 


0 #- 


M.    Open. 


3 


^sd 


-# # &^ 


r  r  r  r  r  r 


f=?=^ 


9^H-J 


J-J  J.J  J  i 


-# — 9- 


rrr^ 


Examples  for  Practice. 


■4-- 


t=t 


£ 


'Jf=X 


=1: 


^: 


22- 


lizqc 


t=t: 


i^ 


• 9- 


?=  =P=f=P=:  =g=:j r-t-p=zp=t=  =t 


g 


-6>- 


•izz=!t±:i 


23. 


m^ft=t=^^^ 


=P=p: 


^^£ 


-fS^— ^- 


t=tll 


29     — 


Further  examples  for  practice  may  be  selected  from  amon^ 
those  under  Exercises  1  and  2. 


The  triad  is  called,  in  contradistinction  to  its  inversions, 
the  fundamental  chord  This  is  the  case  with  every  other 
chord  consisting  of  a  succession  of  thirds.  Major  and  minor 
ti'iads  are  consonant  chords,  because  they  are  not  limited  to 
any  special  succeeding  progression  (resolution). 


B.   The  Dissonant  Principal  Chords. 

§  14. 

DOMINANT  CHORD  OF  THE  SEVENTH. 

If  the  dominant  triad  be  extended  upward  by  adding 
another  third,  a  chord  of  four  tones  is  formed,  a  chord  of  the 
third,  fifth,  and  seventh. 


The  fundamental  (root)  of  this  chord  being  the  fifth  or 
dominant  of  the  key,  the  chord  is  named  the  chord  of  the 
dominant  seventh,  or,  for  short,  chord  of  the  dominant  (dominant 
chord).  This  name,  chord  of  the  seventh,  is  also  applied  to  this 
chord,  other  chords  of  the  seventh  being  more  especially  designated. 
Form  this  chord  in  ail  major  and  minor  keys. 

The  dominant  chords  of  like-named  keys  are  alike. 

The  third  of  the  dominant  chord  is  major,  the  fifth  per- 
fect, the  seventh  minor. 

Its  third  and  fifth  form  the  interval  of  a  minor  third;  its 
third  and  seventh,  a  diminished  fifth.  Its  fifth  and  seventh 
form  a  minor  third. 


—     30     — 

The  natural  and  necessary  progression  (resolution)  of  the 
dominant  chord  is  to  the  tonic  triad.  Because  it  requires  to  be 
resolved,  it  is  called  a  dissonant  chord. 

Because  it  must  resolve  directly  to  the  tonic  triad,  it  is  called 
a  dissonant  princijjal  chord. 

Its  resolution  is  effected  thus  : 

The  third  (leading-note)   progresses  by   a  degree   upward 

into  the  fundamental  of  the  tonic  triad. 
The  ffth  progresses  by  a  degree  downward  into  the  funda- 
mental of  the  tonic  triad. 
The   seventh   progresses   by  a  degree   downward  into  the 
third  of  the  tonic  triad. 
Although  the  fundamental  is  not  restricted  to  any  positive 
progression,  it  usually  moves  up  or  down  (when  it  appears  in  the 
fundamental  chord)  into  the  tonic  (key-note). 


48. 


^m- 


^—n 


7^- 


^=^ 


G—^ 


rrt7 — U^zijo — Ti  ,  — n 


9i 


^. 


^=i 


Form  the  dominant  chord  of  the  seventh,  with  reso- 
lution, in  all  major  and  minor  keys,  both  in  close  and  open 
harmony. 

The  regular  resolution  of  the  dominant  chord  always  pro- 
duces a  triad  [here  a  three-tone  chord  with  one  tone  trebled  is 
meant]  without  a  fifth. 

§  15. 

INVERSIONS  OF  THE  DOMINANT  CHORD. 

The  dominant  chord  has  three  inversions: 


The  tones  of  these  are  led,  on  resolution,   like  those  of 
the  fundamental  chord;  only  that  the  original  root-tone  usually 


—      31     — 

remains    stationary,    when   found  in    an   inner  or  the  highest 
part,  in  order  to  complete  the  triad  resulting. 
The  inversions  are: 

1.   The  chord  of  the  fifth  and  sixth  Q: 

i2: 


60.  S 


Close.  Open.  C. 


O. 


§^^iE 


-dL. 


2.   The  chord  of  the  third  and  fourth  (*); 

(9 79-~rrr\t~ r—&- 


51. 


^^^=t= 


-«5»- 


^^HS^ 


¥^ 


M^- 


52. 


3.   The  chord  of  the  second  (i); 


l^i^fei^i^^l 


-<&- 


I 


m 


H 


The  above  chord-names  are  derived  from  the  intervals, 
which  the  two  tones  forming  the  seventh  in  the  fundamental 
chord  form  with  the  bass  in  the  inversions. 

Name  the  intervals  of  the  inversions,  close  harmony  being 
supposed.  Then  form  each  of  these  inversions  in  close  and 
open  harmony,  in  all  major  and  minor  keys  and  different  posi- 
tions of  the  higher  parts. 


§16. 
TREATMENT  OF   THE  DOMINANT   CHORD. 
From  the  dominant  chord  the  fifth  may  be  omitted  : 


53. 


^^^f 


—    32     — 


The  fundamental  is  oftenest  doubled  : 


51 


^ 


-^ 


i9 & ryGh- 


In  regular  resolutions  a  doubling  of  the  third,   fifth,   or 
seventh  would  occasion  parallel  octaves: 


55. 


g^ 


i^-*-  ^  -•- 


I 


By  omitting  the  fifth  and  doubling  the  fundamental  we 
obtain  four-part  dominant  chords,  which  resolve  to  a  complete 
triad,  and  are,  therefore, very  useful  in  closes: 


I^E 


?g— ^-t=gg=g: 


-Y^—Jszn 


56. 


Form  similar  closes  in  all  keys. 

§  17. 

DIFFERENT  STYLES  OF  CLOSE. 

To  bring  about  a  close,  the  tonic  triad  is  usually  pre- 
ceded by  the  dominant  chord  of  the  seventh,  and  by  preference 
as  the  fundamental  chord,  because  the  progression  of  the  bass 
from  one  root-tone  to  another  renders  the  close  more  firm  and 
decided.  Accordingly,  the  cadences  hitherto  exhibited  generally 
assume  the  following  fonn: 


57. 


33     — 


and  from  No.  7 

4- 


68. 


m 


-25*- 


the  following  close  results: 

J — 4- 


^g=^ 


g: 


Si 


..^, 


-&- 


-^- 


Si 


I        I 


1^- 


which  is  to  be  played  in  all  keys. 

But  the  employment  of  the  dominant  triad  in  cadences  is 
by  no  means  excluded  hereby.  On  the  contrary,  the  triad  often 
takes  the  place  of  the  dominant  chord  of  the  seventh  in  the 
former  manner. 

Many  melodies  are  distinctly  divided  into  sections,  though 

these   are  not  necessarily  marked  by  rests.     It  is  the  part  of 

the  harmony,  to  mark  these  divisions  in  its  own  way,  by  more 

or  less  complete  cadences. 

The   most  perfect   closing  chord  is  one  containing,  both  in 

melody  and  bass,  the  key-note  of  the  scale  : 

Octave  in 
sopr. 


59. 


I 


^^ 


~ «2 I 


-/2i?_ 


This  is  peculiarly  suitable  as  the  close  of  an  entire  com- 
position, although  by  no  means  out  of  place  as  the  close  of 
a  period,  division,  or  movement.     (Comp.  the   air  "America".) 

Closes  having  the  last  note  of  the  melody  on  the  third 

or  fifth  of  the  tonic  triad  are  less  perfect : 

Third  in  Fifth  in 
I          sopr.  sopr. 


60. 


v^- 


'^ 


%- 


-nr 


^^ 


m 


e 


These  are  well-adapted  for  partial  (or  imperfect)  closes,  but 
may  also  be  used  in  the  final  close.     (Comp.  Model  6.) 
B ussier,  Elementary  Harmony,  3 


34: 


Specially  adapted  for  partial  (imperfect)  closes  are  the  pro- 
gressions ending  with  the  fundamental  of  the  dominant  : 


61. 


Similarly  in  Minor, 

At  J,  we  perceive  how  the  sub-dominant  precedes  the 
harmonic  point  of  rest  on  the  dominant,  whereby  the  well- 
known  progression  (sub-dominant — dominant — tonic)  is,  of  course, 
necessitated. 

Such  partial  closes  on  the  dominant  are  called  half-closes. 
Their  employment  depends  upon  the  character  of  the  melody. 
The  following  melody,  for  instance,  admits  of  a  half-close  in 
the  middle. 


62. 


ies 


^ 


3 


:t=t: 


2£e 


-^-25^ 


I     V 


The  melody  harmonized  as  Model  7  farther  on  also  affords 
an  opportunity  for  a  half -close  in  the  middle,  though  it  appears 
more  suited  to  the  character  of  the  melody  to  avoid  such  a  half- 
close. 

Complete  and  incomplete,  full  and  half-closes,  are  to  be 
played  in  various  major  and  minor  keys. 

The  full  and  perfect  close  is  occasionally  followed  by  a  sort 
of  supplementary  close  employing  the  sub-dominant  triad  ;  this 
is  the  plagal  close. 


—     35     — 


a 


i 


S±: 


«: 


-75<»- 


:g: 


^ 


E£ 


63. 


iBE 


£g 


^^13 


IV 


This  is  also  called  the  church  close,  its  peculiarly  solemn 
character  having  been  the  cause  of  its  frequent  employment 
in  sacred  music.  It  sometimes  occurs  without  any  preceding 
dominant  close. 

The  harmonized  ascending  scale  is  more  satisfactorily 
closed  by  the  dominant  chord,  when  this  latter  is  taken  as 
chord  of  the  third  and  fourth: 


64. 


I 


-G--^ 


^^^^^^^ 


¥-b=-— 


ns: 


g^ 


/    / 


^-^i^^ 


:g=l 


15>- 


is 


^M 


/ 


(9- 


-^- 


65. 


i^ 


G ^ 


:s=s: 


& n~ 


t2i=^— g: 


^ 


Play  the  above  scale  in  all  major  and  minor  keys. 

The  employment  of  the  fundamental  dominant  chord  to 
this  end  has  a  less  pleasing  effect: 


"0 7 

/L.                        t^i          <^ 

•3             f??* 

(O^ 

^         «9         ^ 

/^       -^         ^  ■ 

T\*        i-r?        <?'!5'      ^i*                   .-^         ^                      1 

^^                                    «>                                            '^ 

1 

For  inducing  tone-repetition  in  the  melody  the  dominant 
chord  is  also  useful,  as  all  its  inversions  and  positions  can  be 
resolved  against  the  dominant. 


—     36     — 


67. 


"'^~#" 


$^^^^^^^^^ 


I         I 


--{=t 


^t 


->^- 


Execute  the  above  at  the  instrument  in  different  keys. 


§  18. 
DOMINANT  CHORD  OF  THE  SEVENTH,  AND  TONIC  CHORD 
OF  THE  SIXTH  AND  FOURTH. 
The  following  progressions  follow  the  rules  given  in  §  13 
for  the  treatment  of  the  chord  of  the  5- 
I.  II. 


68.  < 


H 


f=r 


? 


^^^^ 


m   "  ^ — •- 


m 


I    I 


I    i 


r  r 


-^^ 


:t=t 


&^^l 


^ 


From  a  combination  of  both  examples  results  the  following 
freer  treatment  of  the  ?  chord,  which  we  shall  use  in  future  as 
occasion  offers  : 


69. 


Ir-r— 1 — H-t— 4 

Here  the  f  chord  enters  freely,  as  at  I,  and  its  higher  inter- 
vals progress  downward  by  degrees  ;  whereas  the  bass,  as  at  IL 
progresses  doAvnward  by  a  degree  into  the  chord  of  the  second. 
E.   g.: 


70. 


J=i5l 


— s-i 


m 


J: 


-&- 


r  r 


I  I  I  I    r 


"^^ 


*- 


1^^ 


-<2_ 


I 


—     37     — 

By  means  of  a  slight  rhythmical  variation  we  obtain  strict 
harmonic  regularity. 


71. 


fe 


:^: 


f=F^ 


i  J 


Such  rhythmical  variations  serve  to  explain  many  free 
harmonic  leadings. 

The  chord  of  the  sixth-and-fourth  between  two  other 
chords  on  the  same  bass,  may  also  enter  in  combination  with 
the  dominant  chord  when  the  fourth  and  sixth  progress  by  a 
degree.  ♦ 


72. 


i 


■a—e— 
I       I       I 


3=^: 


Tr-r 


-(& 6f 


Exercise  7. 

To  harmonize  melodies  in  four  parts,  using  the  domi- 
nant chord  and  its  inversions. 

Model  7. 


rT=rf=rTf 


msM 


uMs$m 


—     38     — 


i 


■• — ^ 


j#afej 


^ 


i 


Examples  for  Practice. 


\^5. 


i^ 


1^^ 


^-^-E^t 


^E£ 


lE^ 


3=* 


Ti=^ 


-*—m — t5? — I — »-\-*^—    I  ^  » — *-t-*  III* 1  r  I — \ 


27.   


t=ti 


tEi^E£:^^^a 


^^'t^ 


l^333S 


*-•-•-'-* 


t^r^,-J^3--3 


^Sg^ 


u    28. 

ate 


^-^^'-^- 


i^^ 


:fc:=i: 


:i=??r:[: 


P— # 


t— i— r 


i=t 


eitiiza: 


r* 


^s 


fei 


29. 


^ 


-G—^-^- 


^ 


2^±? 


^E 


t4 


1— t-* 


=|; 


a^FFfrFf? 


EC. 


EC. 


-B: 


?—, •^ 


— fi' 


-•^ 


:^ — ^  '    r 


?^^ 


-.*=T-<9- 


^^-& 


^ 


:iFi-*- 


ia?-ihr-F 


•zzt 


39 


:te^^^^^ 


t=^t=t4 


^ 


f-^r 


1 


^f^^^ 


w^=r 


-o- 


a 


^^ 


^^ 


Example  of  Tone-repetition. 


EE^Ei^ 


3=:)=t 


S^^gE3ESE^E3ESE3: 


Play  in  all  major  and  nfiinor  keys. 

§  19. 

CHORD  OF  THE  NINTH. 

If  the  dominant  chord   be  extended  upward  by  adding 
to  it  another  third: 


73. 


:|ai8Sa 


we  obtain  a  five-tone  chord  whose  name,  derived  from  its 
in<)8t  (.'xteiided  interval,  is  tlie  cliord  of  the  ninth. 

The  ninth  in  major  being  major,  this  chord  is  called  in 
a  major  key  a  major  chord  of  the  ninth.  The  ninth  in  minor 
being  minor,  the  chord  is  in  minor  called  a  minor  chord  of 
the  ninth. 

Like  the  chord  of  the  dominant  seventh,  it  is  a  dissonant 
principal  chord,  resolving  directly  to  the  tonic  triad.  The  ninth 
is  resolved  by  a  step  downward  into  the  fifth  of  the  tonic 
triad;  the  remaining  intervals  are  resolved  as  in  the  dominant 
chord,  excepting  that  the  fifth  of  the  major  chord  of  the  ninth 
must  be  resolved  upwards,  to  avoid  parallel  fifths. 


M 


^ 


^ 


40 


Although  actual  parallel  fifths  would  not  be  formed,  in 
minor,  by  the  downward  progression  of  the  fifth  (the  first  fifth 
in  the  progression  not  being  perfect),  still  it  is  best  to  avoid 
this  resolution  in  minor  also,  wherever  possible.  The  minor 
mode  exhibits  here,  as  in  other  cases,  a  curious  dependence  upon 
the  major;  that  is  to  say,  progressions  which  are  faulty  in 
major  are  held  to  be  so  in  minor,  and  are  consequently 
avoided,  although  in  minor  the  rules  are  not  transgressed.  To 
an  attentive  listener,  chord-progressions  like  these: 


75. 


I 


IS3SS 


:«?^ 


8-- 


will  afford  convincing  proof.  The  hypothesis  of  so-called 
covered  fifths  and  octaves,  formerly  offered  in  explanation 
of  similar  cases,  is  too  contrary  to  the  nature  of  our  musical 
system  to  find  acceptance  in  a  course  of  composition. 

The  regular  resolution  of  a  five-tone  chord  of  the  ninth 
always  yields  a  triad  with  doubled  third,  thus  necessitating 
an  exception  to  the  rule  given  before. 

The  ninth,  either  in  the  fundamental  chord  or  an  in- 
version,  must   never   be    so   placed   as   to    become   a   second 


-g^ — -  ;  for  the  principle  of  chord -formation  by  successive 


thirds  would  thereby  be  abandoned,  and  the  chord  of  the  ninth, 
thus  stricken  out  of  the  list  of  chords  in  a  limited  sense. 
INTeifher  should  the  two  parts  formin,2:  the  interval  of  the  ninth 
be  mutually  inverted,  so  as  to  place  the  original  ninth  in  the 
lowest  part  and  the  original  fundamental  in  the  highest:  e.  g. : 


^ — 3j —   must  never  become   fe-^zi:=.    It  is  only  necessary 
to  strike  such  an  inverted  chord,  e.  g.; 


76 


to  make  plain  the  need   of  this  rule. 
Notation,   §  133.) 


(Elem.  of  Harm,  and 


—     41     — 

The  ninth,  therefore,  must  neither  be  contracted  to  a 
second,  nor  inverted  to  a  seventh.  —  Hereby,  the  employment 
of  this  chord  and  its  inversions  is  shown  to  be  limited,  and 
the  last  (fourth)  inversion  quite  excluded.  The  serviceable  in- 
versions of  the  chord  of  the  ninth  follow,  in  as  close  harmony 
as  practicable. 


The  ninth  being  excluded  from  the  inner  parts,  there 
remain  to  be  employed  only  those  of  the  first,  second,  and 
third  inversions  which  have  the  ninth  in  the  highest  part. 


79. 


m 


First. 


Second. 


Third. 


i— gg;=i^^gJ 


:s: 


i 


-GC^—OL. 


This  chord  becomes  a  four-tone   chord    by    omitting  the 
fifth;  whereby  the  second  inversion  is  lost. 


y f 

1 

/L                       1 

.._.,   ... 

rrr\ 

^     1 

/O       -    1 

^>              A 

v^;      /v      s    1 

^ 

^         1 

%) 

/?  . 

■•- 

rj        ♦ 

i'- 

c* 

1 

•    J 

'^jf^i     • 

1 

1 

...        f^l^..      w 

^             * 

,,^ 

« 

1 

^                        1 

80. 


Form  the  chord  of  the    ninth,  together  with   ailowabie  In- 
versions, and  its  resolutions,  in  all  major  and  minor  keys. 

By  the  aid  of  this  chord,  the  descending  scale  can  now  be 
well  harmonized  between  the  seventh  and  sixth  degrees. 


—     42     — 


81. 


83. 


y 1 

/f_             /5            ,.                                            1 

ff?\ 

^, 

-a— g- 

-% 

VM7 

Z 

J 

^^!r 

^ 

rv* 

)• 

^ 

<9 

r> 

^ 

9 

/!2 

^           Ki 

—G 

\>|/ 

"     ^ 

-iSh 

C\* 

-  <^ 

i^C/      f^fZt 

'?.          1 

T. 

o       ■ 

J           (y                                               1 

1 

82. 


i^^&^g^ 


1^5 


84. 


ttJ: 


^fe^ 


^^ 


ISE- 


& — &- 


-& — ^ 


m 


^T7     ^ 


The  entrance  of  a  dissonance  of  the  ninth  by  a  skip  in 
both  parts  should  be  avoided  both  in  parallel  and  contrary- 
motion. 

Not  allowable: 

.         .        I     I  I 


85. 


tf  6  2^- 


^ 


*=?^ 


I 


f 


i 


121 


g-* 


■^    4 


aiic^ 


Els 


^ 


i. 


-li-=F^t|=ft 


::^z=Jia] 


J  J 


I     I 


^ 


&^ Ot~9- 


&— 


r^ 


Nearly  as  unallowable  in  contrary  motion: 


1 — r-r 


r^- 


t^& 


-{^ 


?^^E|=ft^ 


a 


a.- 


— t 


J  J 


I 


J  J 


r 


9i::r^^^^|^Eafeg^^gp^ 


Exercise  8. 

Harmonize  the  following  melodies  in  four  parts,  em- 
ploying the  chord  of  the  ninth  and  its  inversions. 


y^ 


1-^; 


—     43     - 
Model  8. 


i 


^m- 


I    I 


9feF 


J.J.  i 


^^ 


P 


1 J 


J^ 


3^ 


G ^ 


!«=•: 


rriTf 


94 


f=! 


,^J.    iUiJ      IJJJ 


Examples  for  Practice. 


5=? 


fS^--^'^ 


t=f 


133.- 


^^ 


:p=q: 


^^^^^^^ 


34. 


H&— ^ 


f^^ 


!•=& 


HC. 


=t^ 


(^-9 


-^^ 


t=l± 


Cadence 


1       35. 


^^^^^^^^^^ 


FF 


£ 


t:=q: 


£r^-^T^ 


t=t 


^ 


—     44     — 


^^3E^^^^^^,, 


§  20. 

MINOR   AND   DIMINISHED    CHORD    OF   THE   SEVENTH. 

If  wc  form,  on  the  seventh  degree  of  the  scale,  a  chord 
of  the  seventh,  we  obtain 


87. 


in  major,  the  minor  chord  of  the  seventh 


1= 


in  minor,  the  diminished  chord  of  the  seventh  ^L^^j^- 

The  minor  chord  of  the  seventh  comprises  the  four  highest 
tones  of  the  major  chord  of  the  ninth;  the  diminished  chord 
of  the  seventh  comprises  the  four  highest  tones  of  the  minor 
chord  of  the  ninth.  Both  are  dissonant  principal  chords,  resolving 
directly  to  the  tonic  triad.  The  resolution  of  the  several  tones 
is  in  both  chords  the  same  as  in  the  chord  of  the  ninth. 


89. 


-6* "- 


¥-^ 


^=^i 


i 


..fe 


The  minor  chord  of  the  seventh  has  minor  third,  dimin- 
ished fifth,  and  minor  seventh.  The  diminished  chord  of  the 
seventh  has  minor  third,  diminished  fifth,  and  diminished  seventh. 

In  the  minor  chord  of  the  seventh,  the  adjacent  toiiefi 
form  the  intervals  of  two  minor  thirds  and  one  major  third: 
in  the  diminished,  three  minor  thirds. 


45      - 


The  inversions  of  both  chords  bear  the  same  names  as 

the  corresponding  inversions  of  the   dominant  chord,  namelv 

90 -^ 


Chord  of  the  fifth  and  sixth 


Chord  of  the  third  and  fourth: 


i^lai^ 


Chord  of  the  second: 


:g=irrt2. 


Igaa 


The  minor  chord  of  the  seventh  and  its  inversions  are 
employed  like  the  chord  of  the  ninth,  inasmuch  as  the  original 
seventh  remains  in  the  highest  part,  the  chord  of  the  second 
thus  being  excluded. 

This  limitation  does  not  bind  the  diminished  chord  of  the 
seventh;  which  can,  on  the  contrary,  be  employed  in  all  its 
positions  and  inversions.  Its  third  inversion  resolves  to  the 
tonic  chord  of  the  fourth-and-sixth,  and  can,  therefore,  be  em- 
ployed only  when  this  latter  can  progress  regularly,  i.e.:  in  this 
case  downward  by  a  degree.     E.  g. : 


91. 


a 


-J- 


9i 


^^- 


r 


^ 


§i 


y. 


-f9- 


A 


i 


G- 


J 


=1= 


r 


e 


I    I 


-^ 


r-t 


i 


Form  both  chords  and  their  inversions,  with  resolutions,  in 
all  major  and  minor  keys.  A/ 

It  is  allowed,  on  resolving  the  f  chord  derived  from  either, 
to  lead  the  original  fifth  by  a  stej)  downward  in  the  highest  or 
either  inner  part,  thereby  avoiding  a  doubled  third  in  the  result- 


ing triad. 


92. 


I 


S 


U^ 


I^. 


f 


^1 


r 


r 


—     46     — 

In  the  diminished  chord  of  the  seventh  the  third,  both  in 
the  fundamental  chord  and  second  inversion,  may  progress 
downAvard  h v  a  degree  when  its  second  diminished  fifth  (as  h-f 
in  the  chord  oi  g^-h-d-f)  is  inverted  to  an  augmented  fourth. 
93. 


Whereag,  in  the  exception  under  No.  92  only  the  seventh 
progresses  downward,  and  the  other  three  parts  upward,  in 
the  above  only  the  fundamental  progresses  upward,  the  other 
three  parts  being  led  downward.  Consequently,  in  harmonizing 
the  scale,  the  minor  chord  of  the  seventh  can  be  employed 
only  at  6—5  in  the  melody;  the  diminished  chord,  however, 
at  2-1,   2-3,   4-3,   4-5,    6-5,    and  7-8. 

Both  the  chords  are  harmonically  better  adapted,  for  the 
progi-ession  7  —  6  in  the  descending  scale,  than  the  chord  of 
the  ninth.  As  we  are  now  for  the  first  time  enabled  to  har- 
monize this  scale,  we  introduce  here,  as  second  chord  before 
the  last,  the  chord  of  the  sixth  and  fourth,  so  that  the  last 
five  chords  form  our  five-chord  cadence  (§  13,  No.  39). 


94.     / 

/^ 

T 

1 1 

rj 

— «s>- 

— ^2— 

—G— 

_ 

W- 

~tr 

-6*- 

4t 

-g;^-^; — ^ 





-*%- 

--w— q 

Major.  < 

%) 

& ^3 

■^G- 

iW 

^^ 



^—^ 6,_ 

— 7? 

__^_ 

—Ot— 

—&- 

—y^— 

1 

—Cl— 

i^j 

/> 

_  G 

rj 

^_ 

..^ 

-o—^—G- 

_ 1 

-G- 

'W 

or: 


—     47     ~ 


96. 


Minor,  J 


fe=g=^ 


'%-% 


t7—sr 


»=!g^3?: 


^ 


ite^a^ 


\ 


w 


lE^ 


~o — rr 


% 


-nr-^ — G 


Q^.  JHei. 


-^m 


m:     97. 


)^ 


3=S=|g=srr; 


pr-.^r-^-pr 


^-^ 


:f_«a^_^_ 


^ 


t 


I 


Play  the  harmonized   scale   by  heart  in  all  keys,  as- 
cending and  descending. 


Exercise  9. 

Harmonize  the  following  melodies  in  four  parts,  em- 
ploying in  major  the  minor  chord  of  the  seventh,  in  minor 
the  diminished  chord  of  the  seventh. 


Model  9. 


I 


I 


U=^J=L-A 


i 


1 


-y^ — « — «- 


s> — G- 


f 


m^pf^f^ij^^^^ 


^ 


—     48     — 


4=E^=F 


N.B. 


J 


spa^s^^^^ 


i 


^E£J 


F^af 


r 


lU  iJJUAAJ 


■H2=|!=*E? 


tte 


!h==) 


^ 


38. 


Elxamples  for  Practice. 


»^eE-E^ 


:^-Tt 


-/«- 


39. 


-,^— ^- 


atzf: 


-z^- 


^ 


3P 


333 


j^^ 


^=t 


-(f5>- 


^=^=i: 


-75^ 


40, 


^^^^^^^^^^ 


St. 


m 


:p=±z=p±t==p=J 


-P # •-  — • # ^ 


p==t=v=(: 


N.B.  Here  the  diminislied  fifth  follows  the  perfect.  Although 
unobjectionable  to  the  ear,  the  eye,  assisted  by  an  unconscious  depen- 
dence upon  the  major  mode,  is  offended  by  it. 


49     — 


i 
i 


m 


^^ 


m 


^t: 


B 


42. 


1^ 


t==t 


:p=HE=|i==^ 


s 


^^g^^^^^^¥^^^:|^^^^E^ 


'^= 


^=P= 


:t=t: 


43^ 


i 


i^@^ 


P^ 


:^ 


ripi:=g,- 


t=:t=:J:=t 


44. 


EBE5 


p — 0- 


■^=.t 


w=t 


P==1==t: 


-&- — •- 


m 


^ 


m 


§  21. 
THE  DIMINISHED  TRIAD. 

If  we  construct,  on  the  seventh  degree  of  the  scale,  a  triad, 
we  obtain  for  major  and  minor  the  sa?ne  diminished  triad. 


faggge 


The  diminished  triad  comprises  both  in  major  and  minor 
the  three  highest  tones  of  the  dominant  chord,  and  is  ti'cated 
like  this  latter. 


99. 


^ 


■^-* 


It  is  an  integral  part  of  each  of  the  other  dissonant  chords 
resolving  to  the  tonic  ti-iad: 


100. 


|^^^=fegiagife 


Bussler,  Elementary  Harmony. 


50     — 


but  is  least  of  all  adapted  for  determining   (fixing)  the  key, 

for  it  may  be  mistaken,  not  only  for  a  subordinate  chord,  but 

also  for  a  fraction  of  some  diminished  chord  of  the  seventh. 

By  doubling  the  third,  it  becomes  a  four-part  chord. 


¥- 


^Sf 


iCl- 


:&=zti-= 


S 


^Pl^ 


101. 


Its    resolution    yields    a    triad    without    fifth,    and    with 
doubled  third. 

Its  two  inversions  are  called,  like  those  of  any  other  triad: 

102. 

Chord  of  the  sixth: 


Chord  of  the  sixth  and  fourth: 


Its  higher  parts  form,  with  the  bass: 

In  the  fundamental  chord,  minor  third  and  diminished  fifth; 

In  the  chord  of  the  sixth,  minor  third  and  major  sixth; 

In  the  chord  of  the  l^  augmented  fourth  and  major  sixth. 

In  resolving  the  chord  of  the  sixth  derived  from  this  triad, 

we  have  the  same  liberty  as  with  the  t  chord  derived  from 

the  minor  and  diminished  chords  of  the  seventh,  namely: 

The  original  fifth  may  be  led  downward  in  the  inner 
parts.  On  account  of  this  double  resolution,  it  may  also  be 
doubled,  but  only  in  this  first  inversion. 


103. 


—     51 


Form  the  diminished  triad  and  its  inversions,  with  resolu- 
tions, in  all  major  and  minor  keys. 

The  chord  of  the  sixth  derived  from  the  diminished  triad, 
may  be  substituted  for  the  domiuant  chord  in  the  ascending 
scale,  No.  64:  the  close  hereby  loses  in  firmness,  but  the  leading 
of  the  parts  gains  decidedly. 


104. 


1=1: 


w---^-- 


}SE^ 


.a 


Exercise  10. 

Harmonize  the  following  examples  for  practice  in  four 
parts,  employing  the  diminished  triad. 

Model  10. 


^fce^^F 


ili 


e- 


i 


i 


Ji 


\ 


»-ft 


r- 


0-*-jd 


•^^•-p- 


i^^i 


-^rt 


f 


f^ 


td: 


rrn? 


a 


t 


—     62     — 


^45. 


Examples  for  Practice. 


tr-T^~» 


^ 


?2":^S 


It: 


t 


£ 


:^:i^ 


=^ 


-&- 


i 


a  46. 


e^ 


iB— •: 


^^ 


=1!^ 


^ 


HC. 


t=t 


^ 


-/2^- 


pzr-nrf 


E^ 


^ 


i 


g— •- 


=F=>=^ 


^— ^- 


i^ES 


t=t 


^^j^gfe^gggs^ffm^.=yifcti 


§  22. 

FEEER  TREATMENT  OF  THE  CHORDS. 

The  pupil,  having  hitherto  employed 

the  chord  of  the  fourth  and  sixth  only  under  special 

conditions  (§§  13,  18), 
the  dominant  chord,  and  chord  of  the  ninth,  only  with 

a  strictly  regular  resolution, 
the  other  dissonant  chords  resolving  to  the  tonic  like- 
wise only  under  special  restrictions, 
is  now  sufficiently  grounded  in  the  elementary  laws  of  chord- 
progression  and  the  modes  to  employ  intelligently  the  following 
free  leadings. 

1.  The  fifth  of  the  dominant  chord  may  also  progress 
upward  by  a  step,  in  any  part. 

2.  To  secure  completeness  of  the  tonic  triad,  the  inteiTals 
of  the  dominant  chord  in  the  inner  parts  are  frequently 
resolved  irregularly,  particularly  at  closes,  being  then  resolved 
to  that  tone  which  would  be  omitted  by  their  regular  resolution. 


—     53     — 


105 


I 


p=d=t=, 


p  **  I  I        I         I       I  r^^ 


^  --J-,  J -^ 


m^m 


r 


f 


r 


^ 


As  the  various  positions  of  the  intervals  of  any  chord 
exercise  an  influence  on  the  harmonic  effect,  such  irregular 
resolntions  of  the  inner  parts  are  often  occasioned  to  bring 
in  some  desired  or  agreeable  chord-position. 


106. 


EE33 


9£ 


An  irregular  resolution  may  also  occasionally  be  allowed 
to  secure  a  better  leading  of  the  parts;  e.  g.-.  to  avoid  mono- 
tonous repetition  of  a  tone  or  phrase: 


107.    I        I        I 


I    I 


P=F=F=FI 


:i 


^P^ 


^ 


I  I      I 


B|     o|    C|       J      0|     J  .1,  J,  !      I      I    J  I      \^±  ♦ 


=ti=t: 


^ 


f 


or  to  give  a  part  greater  variety  of  position: 

I  I 


108. 


^ 


^^ 


u-i^^..y=^ 


^^N^s 


^U-. 


I  I 


m^ 


—     54     — 


But  in  such  cases  only  the  third  or  fifth  of  the  dominant 
chord  may  progress  by  a  skip,  and  not  the  seventh: 
Bad:  Good:  or: 

1 1— J-rp— J      J      J     „        I        I— J- 


109. 


i  J  * 


The  melody  of  the  soprano,  and  the  exigencies  of  good 
leadings  at  the  same  time,  particularly  in  the  bass,  give  occa- 
sion for  like  free  leadings  of,  with  similar  restrictions  for,  the 
soprano.  E.  g.:  if  the  following  leadings  are  found  in  the 
given  melody: 
110. 


S^ 


:^^ 


r- 


# 


^P^ 


they  may,  to  secure  a  good  leading  of  the  bass,  be  harmonized 
in  the  following  manner: 

HI.  I  I 


^^ 

^^ 

fF^"^ 

F=^=3=^i^^ 

-rrrM- 

L- 

— 1^- 

^= 

_  1 

i 

1     1     1 

1      1      1 

^7 

=  ::?z::i 
— tc      ^ 

1 

1 

— •- 

> 

1 

1 

— #--■ 

-#- 

.->'  ^1 

— ] — •—  - 

— 1 1 — 

0 

1^ 

«  1 

— «  J  [1 

1    1    1 
•   •   • 

rr 

f 

8|= 

1 

-1 

1 

^^ — '- 

— n — m— 
1      -1      ^ 

tz«-f 

J_^L_ 

—     55     — 


in  comparison  with  which,   regular   leadings   would   in   most 
cases  seem  awkward,  as  the  following  examples  show: 
112. 


:i 


^^m. 


i=a 


-W-^^^r^ 


r 


III      I 


ggj^ 


I  I 

I J  i 


rr   r 


Jiz:± 


-m — #- 


r 


SEpElt^Ef 


m 


^BB 


^ 


ifp^ 


I 


J:^^: 


rrr 


ipzii: 


i^ 


t=t: 


^^ 


£ 


P=it=« 


3.    The  other  dissonant  chords  resolving  to  the  tonic  par- 
ticipate in  this  liberty  of  leading: 

113.    II  J       I       .  I      ,  J      , 


^^^^^^^ 


^^ 


1 — I — r 


iiJ 


J 


^fe£ 


t 


t 


t=t 


■4i. 


2:fc 


^^S^^ 


In  the  resolution  of  the  minor  and  diminished  chords  of 
the  seventh,  the  skip  from  its  third  downward  to  the  fifth  of 
the  tonic  triad  is  employed,  in  the  inner  parts,  with  peculiar 
frequency  by  the  classic  composers. 


114. 


On  the  contrary,  the  ninth  in  the  chord  of  the  ninth,  and 
the  same  interval  as  seventh  in  the  major  and  diminished 
chords  of  the  seventh,  are  always  resolved  regularly. 

In  the  bass  part  the  pupil  must  take  none  of  the 
liberties  permitted  under  2  and  3. 


—     50     — 


4.  Those  dissonant  chords  resolving  to  the  tonic,  which 
are  eqnally  admissible  in  all  positions  and  inversions,  namely, 
the  dominant  chord  of  the  seventh,  the  diminished  chord  of 
the  seventh,  and  the  diminished  triad,  are  allowed  before  res- 
olution to  alter  their  positions  and  inversions,  provided  that 
the  last  position  or  inversion  so  formed  be  then  satisfactorily- 
resolved. 

115.  a-minor.  ,      |  I 


I 


^^i 


^ 


^ 


m 


art!: 


3t 


M 


fr 


f     ♦ 


# 


i  i 


9i 


:«: 


i 


J^^ 


'^ 


t 


f 


PP5 


Or,  for  the  better  leading  of  the  parts,  the  dominant  triad 
may  be  introduced  in  passing  for  the  dominant  chord  of  the 
seventh. 


116.    < 


iiiii.li 


^^^^f^T^- 


5.  The  dissonant  chords  resolving  to  the  tonic  triad  may, 
before  resolution,  alternate  with  each  other  and  with  the  dom- 
inant triad  (as  a  substitute  for  the  dominant  chord  of  the 
seventh),  provided  that  the  chord  last  employed  shall  be  satis- 
factorily resolved.  —  In  such  cases,  neither  the  ninth  in  the 
chord  of  the  ninth,  nor  the  seventh  of  the  minor  chord  of  the 
seventh,  should  be  led  downward. 


f 


:*=P 


SiE^ 


Jj    iki    i 


n 

IgJg^Si^ 


57     — 


rrp 


r  T 


m 


m 


^ 


:pf=-tt=p 


m 


118. 

Not 
thus: 


1 

^    u 

1 

But,  when  this 

melody  is  given, 

thus: 


The  chords  in  Chap.  11.  will  render  better  leadings  possible. 


6.  The  third  of  the  triad  may  also  be  doubled,  to  benefit 
the  melody  or  the  leading  of  the  parts,  when  the  resolution 
of  the  preceding  chord  does  not  demand  it. 

^  Haydn,     f 


119. 


2^ 


i^l^^ 


m 


^_  *  *     ^  * 


:i=t 


-tr=t 


tei^^^i 


7.  The  fundamental  of  the  dominant  chord  may  progress 
to  any  interval  of  the  tonic  triad.  But  here  the  Rule  must  be 
observed,  that  in  parallel  motion  the  second  should  never 
progress  to  the  unison,  or  the  seventh  to  the  octave. 


120. 


Wrong: 


=S.^r-t- 


^ 


1 


^^m^m 


-^— 


igmzi^ 


i^e 


—     58     — 


The  classic  composers  wrote  such  progressions  even  more 
seldom  than  parallel  fifths  or  octaves. 


8.  The  chord  of  the  fourth  and  sixth,  as  an  inversion  of 
the  dominant  triad,  has  already  occurred  in  free  leadings  with 
a  skipping  bass.  (Comp.  5,  above.)  The  tonic  and  dominant 
chords  of  the  fourth  and  sixth  take  the  like  liberty,  where 
the  bass  moves  in  intervals  belonging  to  those  triads;  the 
higher  parts  may  then  also  change  their  position: 
121. 


wm 


4—1- 


^^ 


=F 


^1 


^=s=t 


fi 


m 


=e 


S 


and  also  when  the  resolution  of  the  J  chord  is  retarded  by- 
similar  harmonic  progressions  in  the  bass,  the  higher  parts,  or 
all  parts  together: 
122. 


4^^-^ 


4=it 


i 


^ 


:^ 


r^^- 
^ 


:p — F~^ 


^^m 


I         I 


^ 


m 


59     — 


The  4  chord  may  follow  the  chord  of  the  ninth,  as  well 
as  the  chord  of  the  seventh  (No.  72). 


123. 


m^ 

\ 

r"^ — 7j — 

/■> 

^ 

The  4  chord  is  also  introduced  by   a   skip  in   the    bass 
between  dissonant  chords  resolving  to  the  tonic  triad. 


^^ 


1 — r 


5^=5*a< 


1 — 1 — r 


124. 


1 — r 


t=t: 


S^ 


Ji4 


g^gj^a 


Examples  like  these,  where  the  bass  reaches  the  |  chord  by 
a  skip  wpivard  and  then  progresses  degreewise  downward,  are 
most  favorable.  Less  so  are  those  in  the  opposite  direction,  or 
when  the  bass  continually  skips  : 


^^^: 


^§1^ 


9.    To  secure  a  better  leading  of  the  parts,  tones  other 
than  those  already  designated  may  be    omitted,  as : 

'126.'        ,ti 


The  thwd  of  the  dominant  chord, 


m 


127. 


Third  or  seventh  in 
chord  of  the  ninth, 


m=i-4-HT-n 


£L 


@i 


m 


—     60     — 


Third  or  fifth  in  the  minor  and  diminished  chords  of 
the  seventh. 
10.    The  progression  of  fifths,  perfect  to  diminished, 


128. 


32: 


^^ 


p        d         p        d 

is  always  correct,  though  the  uptvard  progression  gives  rise  to 
the  scruples  mentioned  under  Model  9,  having  like  origin 
with  those  under  No.  75,  p.  40. 

The  progression  of  fifths,  diminished  to  perfect,  upward  , 
is  very  common  between  the  ttvo  highest  parts, 

i 


129. 


although,  between  the  bass  and  a  higher  part, 


130. 


m 


'^ 


it  is  avoided  by  the  classic  composers,  its  occurrence  with  the 
latter  being  rare;  whereas,  modern  masters  often  employ  it. 

The  progression  of  fifths,   diminished  to  perfect,    down- 
wards    is   also    avoided,   and   is   so  rare  between  bass  and 
soprano  that  it  may  be  designated  as  inadmissible: 
131. 


Inadmissible : 


r:^"g=i 


^. 


likewise  to  be  avoided  between  sojjrano   and  an  inner  part,    or 
bass  and  an  inner  i)art : 


—     61     — 


132. 


iSf-mi^ 


though  admissible,  by  way  of  exception,  between  two  inner 
parts: 


133. 


9^ 


11.    The  seventh  in  the  minor  chord  of  the  seventh,  and 
the  ninth  in  the  chord  of  the  ninth,  may  occur  as  an  excep- 
tion in  an  inner  part. 
134. 

^=*3SB 


•^  ^    ,    ,  ffl  ^    .    ,  J    j    ,  , ,^kJ 


m 


¥^m 


&- 


-^- 


-■g- 


m 


i±: 


m 


?^ 


g: 


r—r^ 


-»- 


^^ 


ij 


4A2 


m 


feE3^El; 


is: 


is: 


I 


a  J 


£: 


is: 


-lu- 


-G 


-Kh 


I 


m 


^i 


z^Jai 


In  the  above  cases,  the  resulting  unusual  positions  are 
generally  induced  by  the  foregoing. 

On  account  of  their  great  frequency,  all  these  liberties 
find  their  proper  place  in  this  first  section  of  the  science  of 
composition;  the  pupil  will  immediately  comprehend  them,  the 
more,  as  he  is  familiar  with  them  from  the  practical  side. 
Their  correct  employment  naturally  depends  upon  the  pupil's 
musical  judgment,  which  will  have  been  essentially  strengthened 
by  the  preceding  exercises. 


—     62     — 

Exercise  11. 

Harmonize  the  following  melodies  in  four  parts,  in 
major  and  minor,  with  the  seven  principal  chords  and  their 
inversions,  occasionally  employing  the  liberties  allowed  in 
the  treatment  of  the  same. 


Model  11.* 


N.B. 


mj-^m^ 


fc£ 


u 


^^ 


3 


I 


9i^f 


f 


-fj-ff 


T 


^ 


f=^ 


t 


^  ^,^     jN.B.    I      I    J  1^^-^      IN.B.  N.B.      N.B. 


N.B. 


*■ 


* 


N.B.  here  indicates  a  place  where  one  of  the  free  leadings  per- 
mitted has  been  employed. 


—     63     — 


Examples  for  Practice. 
As  far  as  the  rules  permit,  the  pupil's  aim  and  endeavor 
should  be  to  write  an  hannonious  or  even  expressive  bit  of 
music,  hut  not,  unless  this  should  be  specially  required,  to 
employ  to  an  extreme  the  devices  last  explained.  The  exam- 
ples are  so  arranged  as  to  necessitate  their  sufficiently  fre- 
quent use. 
48. 


E 


;=i- 


:^z 


-t 


^^^^m 


* 


^^^El; 


=t 


SI- 


* 


49. 


^E^^^E^ 


mmm^^ 


:t=t 


i-J_fi2- 


^^giBl^iP 


-.^-S#- 


t=5t: 


m 


50. 


^^^M^^0^^^ 


m^^^^^^ 


IS 


51. 


'^■e^^E3: 


=i=F=i- 


^W=t 


S:^ 


&feE3 


S^E^EJEJEgE^g^EB: 


iti: 


52. 


fcS 


^^ 


-«5»- 


:^,^- 


:«: 


t=zz^jut=t=:: 


53. 


—     64     — 


^ 


^s=F 


m- 


00.  fj.   li  * 


t=± 


1^3^ 


\^=i=ir 


-&— 


f^^r^=f=^ 


h 


l^E^ES^EB 


SH 


*  '  ^- 


f^^^ 


ta 


tn«: 


3t:iat 


56.  ^_^^^ 


.«|^^=FSS: 


^^^^^ 


T^ 


t^t 


t=F=t 


|M^ 


^^m 


-<2-» 


4=4: 


_6li- 


The  Subordinate  Chords. 

§  23. 
MAJOE   AND   MINOR   SUBORDINATE   CHORDS. 
If  we  torm  a  triad  on  each  degree  of  the  scale 

n    ni 

135.    ^ 


n    ni vr 


we  obtain  in  major,  besides  the  four  principal  triads  already 
known  to  us,  three  minor  triads  on  the  second,  thirds  and 
sixth  degrees;  and  in  minor, 

II     in  VI 


136. 


p 


^ ^ — -e- 


9r 


-I— »S g3=g: 


—     65     — 


besides  the  principal  triads,  a  diminished  triad  on  the  second, 
an  augmented  triad  on  the  third,  and  a  major  triad  on  the  sixth. 

Of  all  these,  the  major  and  minor  triads  are  employed  as 
independent  chords.  Thus  we  have  gained  in  major  three  neiv 
chords,  in  minor  one.  (For  the  present  we  take  no  notice  of 
the  triads  on  second  and  third  in  minor). 

Within  the  key,  the  subordinate  triads  chiefly  serve  as 
connecting  links  between  two  principal  triads  with  each  of 
which  they  have  tivo  tones  in  common;  thus: 

Between  dominant  and  tonic;  between  tonic  and  sub- 
dominant. 


137. 


I 


s>- 


g: 


g 


-XL- ^ ^_ 


-<^- 


..Ct- 


I 


m    I 


S^^l=iii 


-^i 


-G- 


I    VI    IV  I     VI    IV 

Under  like  conditions,  the  subordinate  triad  may  also  con- 
nect principal  consonant  and  dissonant  triads,  in  which  case 
the  dominant  triad  again  asserts  its  right  to  represent  the 
dissonant  principal  chord: 


138. 


''F^=^^ 


-& 


^ 


^m 


-G G- 


1 


12.     £i. 


X^ 


l^^kl 


n 


IV      II        g  II         g  II         7  II  6 

All  these  interconnections  are  founded  upon  a  bass  de- 
scending by  thirds.  The  inversion  of  this  progression  by  thirds 
to  one  by  sixths  should  be  avoided,  as  it  contradicts  the  idea 
of  connection  or  mediation  by  aiming  beyond  the  commendable. 

B ussier.  Elementary  Harmony.  5 


—     66     — 


The  interconnection  of  the  chords  in  the  reverse  direction 
—  sub-dominant  with  tonic;  tonic  with  dominant  —  does  not 
bear  the  character  of  a  mediation,  but  has  rather  an  unex- 
pected effect. 


139. 


^ 


:g=) 


-^t=^=%- 


g^^^l 


31 


IV      VI       I 


III 


m 


IV    VI      I 


This  effect  is  caused  by  the  fact,  that  the  bass- tone,  which 
enters  decidedly  like  a  thirds  is  treated  by  the  other  parts, 
contrary  to  its  nature,  as  a  fundamental.  Where  an  unex- 
pected effect  is  in  place,  such  a  succession  of  chords  is,  of 
course,  justifiable. 

Except  in  their  capacity  as  connecting  links,  subordinate 
ti-iads  are  placed  in  the  foreground  only  in  solemn  vocal  music, 
to  call  to  mind  the  ancient  church  style.  By  Handel  and  Bach 
they  are  employed  partly  to  this  end,  partly  as  influenced  by 
the  leading  of  the  parts;  seldomer  in  the  Haydn-Mozart-Beet- 
hoven period,  because  the  composers  sought  harmonic  variety 
more  in  modulation. 

For  employing  these  chords  the  rule  given  in  §  5  holds 
good,  tliat  tliey  must  he  connected  with  each  other,  or  the  prin- 
cipal chords,  through  common  tones. 

Those  subordinate  triads  which,  considered  as  tonic  triads: 
belong  to  related  keys,  possess  one  tone  in  common;  e.  g.,  in 
C-major,  the  a-minor  triad  and  the  e-minor  triad;  or  the  a-minor 
triad  and  the  (Z-minor  triad. 


140. 


I 


^ 


-• — -L 


a      d 


^ 


^ 


—     67     — 


By  employing  inversions  of  the  principal  chords,  such 
successions  of  triads;  as  are  founded  on  a  bass  ascending  by 
thirds  (No.  139),  lose  their  uncertain  character. 

J 


141. 


km^4^^^ 


WB 


g 


1 


I  ^  < 


VI     I 


£ 


II  I 

IV 


The  triad  on  the  second  degree  bears  the  same  relation  to 
the  dominant  triad  as  does  the  sub-dominant  triad  (§  8).  Under 
the  same  conditions  it  may  precede  the  dominant  triad,  but  can- 
not follow  the  latter.   (II— V— I=IV— V— I,  V— II=V-.IV). 

3^ 


142. 


I 


J 


5=t 


but  not 


3S 


^m 


As  useful  piano-practice  in  all' keys,  and  as  a  prepara- 
tion for  Exercise  12,  the  bass  of  the  following  example  de- 
mands the  principal  and  subordinate  triads  ;  the  position  of  the 
higher  parts,  and  close  or  open  harmony,  being  chosen  at 
pleasure.  It  begins  with  the  dominant  triad.  We  cannot 
employ  this  bass  in  minor,  not  having  as  yet  learned  the 
treatment  of  the  subordinate  triads  II  and  III. 

143.  Minor. 


^ 


-— fi>— ^-h 


n 


— &- 


The  Cadence  (No.  58)  may  be  extended  by  interpolating 
the  subordinate  triad  VI  as  second  chord,  between  tonic  and 
sub-dominant.    Play  it,  in  this  form,  in  major  and  minor. 


—     68     — 


Exercise  12. 

Harmonize  the  following  melodies  and  basses  In  four 
parts,  using  the  fundamental  form  of  the  subordinate  triads. 

In  harmonizing  the  basses,  a  good  leading  of  the  soprano 
should  chiefly  be  kept  in  view. 


Soprano  given. 


Model  12. 


jJ.  1.  'A  J-J-X^'-4^4:«M:^ 


la  J  j 


rf*^=^ 


I 


^t:z3L 


tfed^g 


S — * 


S 


gg^3^^ 


^t 


rf 


f=f 


f 


Bass  given. 


^^^ 


-n 1 V- 


—     69     — 


57. 


Examples  for  Practice. 


b^-^ 


t=T 


P=^ 


^^^^S 


i 


feS: 


atizat 


:^: 


i* 


^tzfc^zjzztz* 


t=1=q=4 


^ 


i 


^S3^ 


^ 


:t:=zfc 


t=l: 


-J!Zzi:t 


i^g 


SET' 


EiEi 


i 


«9 (©-  -r-&—^-  I— (® 


:[={: 


t=t==i 


:^=4=rt=ij: 


ig'-^ 


£ 


-<u- 


I 


P 


i::4=t 


£^^;e? 


*=t 


-w — •- 


^^ 


—     70     — . 


^^^^^'trmmti^^^ 


^m^'^irh^^^^r=f=M=^f^ 


fe^; 


5=l=!=F=t=l 


I 


93 


P^^- 


-<_<_lL 


att 


:tit± 


j^=M 


E^^iggii^^ 


-»—»- 


t=t: 


IpdjE 


fct 


W 


64. 


m^ 


^=t- 


s     s 


33^ 


EEt 


32=5=1 


^S 


f 


y~F~F 


t=t: 


*  I  » 


^E0 


^.    65.  


p— #- 


___^  66. . 


-!(9 — •— •- 


r-|— r 


^^^=r^' 


a^ 


^ 


^— #- 


^^it 


^E^-^-^- 


^ 


^ 

s 


^ 


68, 


S^ 


^^ 


£ 


s 


^ 


—     71     — 

69. 


m 


1=^ 


^^m^^ 


m 


53Et 


=9^: 


1^ 


70.--^- 


m^^^~=^^^^^^^^^ 


J2l 


71. 


ate^g^^^jj-T-^qj^-ff 


^is 


^-n-r^^ 


-^—m- 


^m 


'&— 


§24. 

INVERSIONS  OF  THE  SUBORDINATE  TRIADS. 

In  employing  the  chords  of  the  sixth  derived  from  sub- 
ordinate triads,  the  pupil  should  at  present  restrict  himself  to 

those  uses  justified  by  tlie  relationship    of  the  keys    or   by   the 
degreewise  progression  of  the  bass  : 


144.    <^ 


^^^: 


^ 


^m 


H 


.rr^ 


^ 


The   employment   of  I  chords   derived   from   such  triads 
must  he  strictly  regulated  by  the  rules  given  in  §  13. 


145.    < 


^^^^^ 


^^^^fH=H 


9ti 


*       ^ 


i 


^f  r  " r  '  r  r 


—     72     — 


The  immediate  succession  of  ttvo  chords  of  the  fourth  and 
sixth  is  in  no  case  admissible. 

For  the  employment  of  inversions,  the  requirement  of 
common  tones,  of  course,  still  holds  good. 

Exercise  13. 

Work  out,  with  these  inversions,  the  following  examples 
for  practice,  and  also  some  of  the  melodies  given  in  the 
last  Exercises. 

Model  13. 


I 


fa#j#j^ 


tx 


■*-d-* 


i:  \JiiJ 


V   ^Vri^ 


y^ 


-^ 


^^¥P^ 


t 


P-0 


W^^^ 


";MUi^u^ 


^ 


-r^-[\u 


£? 


f^ 


Examples  for  Practice. 


-:r-=mr-\ 


-X=-^- 


:t=t:l 


^—^ 


-t=x 


n^ 


^ 


t=t=t=t: 


■^M^^^ 


!Ef=^=t4=Efeg{^ 


» ^ 


^^ 


—     73     — 


74. 


m^^^^^ 


-i^«- 


att 


S 


^^^ 


m 


w — m — V 


§  25. 
SUBORDINATE   TRIAD    ON   THE   SECOND   DEGREE 
IN   MAJOR   AND   MINOR. 
The  triad  on  the  second  in  major  still   requires  special 
consideration.     It    may    enter,    as   a   substitute   for   the   sub- 
dominant,  in  full  closes,  half-closes,  and  similar  leadings,  when 

the  leading  of  the  melody  or  parts  offers  opportunity  (No.  142). 
146. 


^^ife^ai^l^il 


m- 


-^M— 4 


lEl^ 


:trdr:i 


t=. 


^1 


^i=i^ 


:f=i= 


I 


In  such  cases,  its  chord  of  the  sixth  (the  first  inversion 
having  the  sub-dominant  of  the  key  as  bass)  is  far  more  fre- 
quently employed  than  the  fundamental  chord. 

This  preponderance  of  the  chord  of  the  sixth  results  from 
the  development  of  our  musical  system,  in  which  this  chord  is 
evolved  from  the  sub-dominant  as  a  chord  of  the  sixth  based 
on  the  latter.  For  this  reason,  the  bass  may  be  doubled  with- 
out hesitation,  although  the  third  of  the  fundamental  chord  ; 
thus  in  a  cadence,  as  a  substitute  for  the  sub-dominant  chord  : 


147. 


■w: 


^ 


I 


^i 


—     74     — 


In  this  capacity  it  may  follow   the   tonic  triad  directly, 
although  possessing  no  tone  in  common  with  the  same. 

I 


148. 


I 


i 


^^ 


^ 


^ 


5 


^: 


The  diminished  triad  on  the  second  degree  in  minor  may 
be  treated  in  a  precisely  similar  manner,  excepting  that  its 
fundamental  chord  occurs  less  often  than  that  of  the  minor 
subordinate  triad  on  the  second  in  major.  Still,  the  funda- 
mental position  is  not  excluded,  but  quite  justifiable  when 
brought  about  by  a  good  leading  of  the  parts: 

149. 


'^^^^^^^^m 


sf=F=1= 


^ 


m 


Vj.^!       r— j: 


-i — r 


4— J 1 


m 


Egaas 


-^ — • 


*  4-  "  -i- 


1^  I 


J=?=8: 


asm-r-r-ni^i 


^ 


^ 


3^ 


The  fundamental  chord  II  may  likewise  follow,  but  not 
precede,  the  sub-dominant  triad  in  the  cadence: 


150. 


\ 

i 


fcmWj 


:£ 


^^^-f-t^-fl 


—    75     — 

Form  cadences  with  this  chord  in  all  major  and  minor 
keys. 

The  I  chord  derived  from  the  tiiad  on  the  second,  though 
occurring  exceptionally  in  like  capacity,  is  here  excluded  by 
the   prohibition    of    successive  chords    of   the    fourth-and-sixth. 

As  the  diminished  subordinate  triad  on  the  II  in  minor 
is  not,  like  the  dissonant  principal  chord  VII,  limited  to  one 
resolution,  it  can  progress  to  a  dissonant  principal  chord  other 
than  the  dominant  chord. 


151. 


^^^ 


m^^^ 


For   the    harmony    of   the    descending   scale   in   major   and 

minor   the   following   smoother  close  results   from  a  degreewise 

pro  egression. 

(§22,2)  ,         ^ 


152. 


1^ 


^-^-^ 


m 


-6f- 


i2=Sg=s 


:# 


5E 


^^ 


ffi 


:si 


9        i 


-<5>- 


§  26. 

SUBORDINATE   TRIAD    ON   THE   THIRD   DEGREE 
IN   MAJOR. 
The   subordinate   triad   on  the  third  degree  In  major  is 
employed   in   a   peculiar   manner   as   harmonic   basis    to    the 
descending  seventh  of  the  major  scale: 

6 

153. 


^ 


immediately   preceding   the    sub-dominant  triad,   although  not 
connected  with  the  latter  by  common  tones. 


—     76     — 


164. 


i 


9^ 


% 


ii= 


g 


m 


Its  /?r5^  inversion  may  be  treated  similarly,  but  only  where 
the  bass  progresses  by  steps. 


155. 


i 


is:: 


-& — && — ^ 


5i 


•:zg?_g__X_ 


«9- 


The  scale-progression  may  also  be  slutted  to  an  inner  2)cirt. 


156. 


^^- 

^-. 

^          /<2 

iP 

— W— 

-^*— 1 

_G^ — j 

tsa      ^.~"  ^          "   ^    1 

/y   , 

iT3 

y^- 

c^ 

2? 

fi*               1 

%/ 

■<5>- 

<2 

V 

•Gh 

rv* 

Z. 

— ^       1 

/^                         II 

^ ). 

~  <>  ■ 

■        _,            />          <^                         II 

-f 

^. 

/^          "^ 

rj         II 

1 

11 

Play  descending  major  scales  with  these  progressions. 


Exercise  14. 

The   following    examples   afford   opportunity  for  em- 
ploying what  has  been  learned  in  the  two  last  §§. 

Model  14. 


I 


feE 


n 


'G G 


ryrff^rf 


J  J 


9^^ 


i^ 


^ 


Etr±± 


±=1= 


m 


77 


«— ^ 


J  J  J  i  J  'J 


fi*- 


g 


9^ 


11—^2 


t9 ^«- 


1 — r 


Poco  allegro. 


m 


^^^i^feE^^sasi 


^^fW^^ 


i=|: 


la 


£ 


^UL. 


^^^^ 


^ 


f 


^ui^rt^ 


F=f 


Trn 


i 


fcz 


r^ 


Examples  for  Practice. 


^75.  „  u    76. 


p 


Is8 


s*i^ 


-f^—f9- 


3=q: 


t=t: 


£i^£^^J 


/SiL ,. 


t=t 


y 


P 


M: 


77. 


iEi 


^m 


—     78     — 


i 


ji  78. 


t±t: 


-&S^ 


m 


79 


m 


-F— • 


80. 


?=4: 


i 


4-^^-J- 


f* 


±==1: 


]==i:: 


tH — i • • F 1 


^— fe^ — • — • — » 


I 


I 


81. 


^ 


EBE3EteE3 


J^E 


J    4    Jt 


-9 ^ 


-^t  r  f  |r  r  r-U-^^^^^^^ 


§27. 
OTHER  FREE  LEADINGS  OF  THE  SUBORDINATE  TRIADS. 

As  the  subordinate  triads,  though  without  contradicting  it, 
do  not  express  their  close  relation  to  the  key  so  distinctly  as  the 
principal  chords,  they  may  enter  into  some  further  combinations 
with  these  latter,  even  without  common  tones,  which  are  justi- 
fied by  the  leading  of  the  parts,  and  often  occur. 

Where  the  dominant  triad  follows  the  subordinate  triad 
II,  the  latter  must  be  followed  by  the  tonic  triad.  (P.  67, 
No.  142). 


157. 


I  I 


P^ 


Here  the  interpolation  of  the  subordinate  triad  III  between 
dominant  and  tonic  is,  however,  permitted  under  the  condition 
that  its  fifth,  having  been  the  leading-note  before,  shall  pro- 
gress to  the  tonic  by  a  step  upward. 


—     79     — 


158.    I 


M^^ 


'f=f^f=f=^f 


H- 


I        I 


^^m 


II 


III 


^ 


-<!5> Tl 


n    V     III    VI 


In  the  progression  VI — III — IV  (Nos.  154 — 5)  the  lead- 
ing I — V — VI  is  allowed  in  major,  when  the  higher  parts  pro- 
gress by  steps  ;  but  7iot  in  minor,  on  account  of  the  augmented 
second. 


159. 


^ 


i=s 


I   I 


m 


^ 


-^- 


-p— 


The  progression  VI — V  also  occurs  in  major  under  like 
conditions,  when  the  higher  parts  progress  in  contrary  motion, 
in  which  case,  too,  the  chord  of  the  seventh  may  be  substituted 
for  the  dominant  triad. 

4 


160. 


Cautious  use  may  be  made  by  the  pupil  of  these  free  lead- 
ings  in   the   examples   for    practice    under   the   next   Exercise. 


§  28. 

SUBOEDINATE   CHOED    OF   THE   SEVENTH   ON" 
SECOND   DEGREE. 


THE 


By  forming  chords  of  the  seventh  on  all  degrees  of  the 
scale  we  obtain,  besides  the  two  principal  chords,  five  subordi- 
nate chords  of  the  seventh  : 


—     80 


II 


1^^=1=1 


161. 


I 


m. 


-i=l! 


l^t 


[=^- 


-ft-o- 


of  which  we  already  employ  one  (that  on  the  second)  in  our 
exercises,  leaving  the  others  for  later  instruction.    (§  67.) 

The  subordinate  chord  of  the  seventh  on  the  second 
degree  in  major  has  a  minor  third,  perfect  fifth,  and  minor 
seventh;  in  minor,  a  minor  third,  diminished  fifth,  and  minor 
seventh.  Like  the  subordinate  triad  on  the  second,  it  occurs 
as  a  substitute  for  the  sub -dominant  triad  in  cadence  and 
similar  leadings,  and  likewise,  by  preference,  in  the  first  in- 
version. 

Its  seventh,  the  key-note  of  the  scale,  must  be  prepared, 
i.  e:  must  be  already  present  in  the  preceding  chord  in  the 
same  part. 

Introduction  of  the  subordinate  chord  of  the  seventh. 


i 


-^- 


Tglr 


O^— j: 


-Ki- 


-t9 


*;g=--i==a 


::=r^3^— i 


li 


:£: 


-O- 


:tiz:=2: 


162. 


"9=^^ 


-i: 


=^^=^* 


-a- 


feiai 


^ 


§ 


:^i= 


4: 


But  it  suffices,  when  such  preparation  is  incompatible 
with  the  requirements  of  the  melody  and  a  good  leading  of 
the  parts,  if  the  seventh  is  simply  present  in  the  preceding 
chord: 


81     — 


163. 


'^m 


isadikhHJ 


^^f-t 


I      '      I 


^ 


Ji4 


I  cL 


9t 


^^1 


:^=t 


-«~^ 


tii 


m 


^. 


§;J^ 


r — 

In  its  progression  to  tlie  dominant  chord,  the  seventh  of 
the  subordinate  chord  of  the  seventh  must  progress  by  a  step 
downward  into  the  third  of  the  dominant  chord. 

Resolution  of  the  subordinate  chord  of  the  seventh 


164. 


I^B 


^5:=^^ 


"w 


^^^ 


£i.      H.   ^ 


gE 


6* ^ 


^^^ 


'^H^,- 

£^2; 


II 


In  the  i^rogression  to  the  |  chord,  the  seventh  is  sustained 
in  the  same  part. 


165.  J 


^m 


r 


EE^Eji^I^ 


1^ 


^ 


i 


i^ 


But  when  the  leading  of  the  parts  is  otherwise  good,  this 
rule  may  be  slighted. 


166. 


P^^^^^ 


^ 


Of  the  two  inversions  of  this  chord  not  yet  mentioned, 
the  chord  of  the  third- and- fourth  may  be  admitted  occasionally, 

B  ussier,  Elementary  Harmony.  6 


—     82     — 

where  no  parallel  fourths  between  the  bass  and  another  part 
result  therefrom: 


Permitted  as  an  exception. 
167.    j^         I     , 


3 


Inadmissible. 


:^si^E3: 


^-^^ 


■^ 


#=f: 


-i5>- 


r"^7 


w^ 


& 


g-^^-l-g-tl 


£^ 


^;;:?^=s^^ 


^ 


e 


t=t 


but  the  chord  of  the  second  07ily  when  it  resolves  directly 
and  quite  regularly  (bass  a  semitone  downward)  to  the  disso- 
nant principal  chord  ;  e.  g.  :  to  the  f  chord  derived  from  the  do- 
minant chord  of  the  seventh: 


168. 


P- 


1^ 


g: 


^=f=g 


1 


9t 


'^ 


-^^ 


Form  full  and  half-closes  with  the  subordinate  chord  of 
the  seventh,  with  various  positions  of  the  higher  parts,  in  ail 
major  and  minor  keys. 


169. 


£ 


^^^T^ 


?^=FF 


-&~i^ 


t=t 


t=1: 


^ 


5S 


S^ 


-■ir=:^ 


-^- 


2i 


3^ 


83 


Like  the  subordinate  triad  on  the  second,  the  subordinate 

chord  of  the   seventh  in  major  and  minor  may  also  progress 

to  other  dissonant  principal  chords  besides  the  dominant  chord, 

the   seventh   of  the   subordinate   chord    of  the    seventh   then 

always  resolving  dowmvard  by  a  degree. 

Subord.  chord  of  the 
170.  seventh. 

Minor.    Subord.  Triad.  ,  |       j 


N4'^H^^^P#iN^^^ 


^^£ 


q=± 


-\—^ 


=^Eg 


P 


6^3^^^ 


Major.    Subord.  chord  of  the  seventh. 
-     ^ I      i     U: 


^ 


^^ 


i>=i==^ 


^m-^^ 


»: 


^  I       I 


J-^  I       I 


iF^^i^ 


9i 


^^m 


■x=x 


The  chord  of  the  second  derived   from   the   subordinate 
chord  of  the  seventh  may  also    make  the  same  movement. 


171. 


^^gg^ 


P^ 


-U.A 


r  r 


pi 


r^^=n 


m 


^ 


^^ 


Exercise  15. 

Work  out  the  following  melodies,  employing  all  chords 
thus  far  learned;  the  first  six  with  special  consideration 
of  the  subordinate  chord  of  the  seventh. 


*  In  the  explanatory  examples,  new  clefs  annul  the  preceding 
signature  without  express  cancellation. 


—     84     — 
Model  15. 


w 


in,^_A4=r     I     '     '      I    F=k= 


r=e: 


^t 


P 


i^ 


3 


5 


^ 


i 


'fJ^fi? 


:^ 


^- 


rrt^ 


J-^ 


i^ 


^1 


-0 — 0 — ^ 


:fe5! 


i 


rrrT^r 


—     85     — 

Examples  for  Practice. 


i 


^^^^i^^^ 


i±^f=t 


^^^^^^^m 


W=i=^- 


t=t 


84. 


p 


'8^=?^ 


p     •- 


^ 


ij-M-A-.  rf=HEfE^ 


t=t: 


:y 


s^^^ 


E^F=P=r^ 


t=tt 


:f=f: 


¥ 


fci=* 


|te£ 


::^ 


85. 


^  86. 


3t=t=i 


^Et^^ee^ 


-^^^^^^^^^^^m 


-• — m- 


-I    I    I    r=}=^ 


g 


90. 

4i 


^Jpe^Ep^feE^E^Jd^J^^^^^ 


—     86     — 


mfr=^=^- 


^ 


^ 


91. 


g:c-J-J  J-r+J^^^S;3E3^^i^p^ 


-p— •- 


1^ 


92. 


-• 0- 


t=t 


93., 


42: 


-(5»- 


^3=i=F=;? 


ESS: 


(5  chords.) 
94., 


u 


t=T=^ 


:±=1=i 


J    f    • 


-    <5>- 


-?5H 


<g-z? — <g— f^ 


Qe^: 


(5  chords.) 


(2  chords  to  each.) 


P 


y-: 


:S=<: 


3.=r=F4-7=i=i 


tit^ 


-• ^ • i^ ^-4- 


95. 


-S    - 


l>= 


t—f— r 


-#— •- 


1=t: 


§1 


i 


fees^^^^s^^^^ 


97. 


:P 


S=»= 


i:=t=t 


S 


—.-A 


t==tzt=t 


^ 


^^f-^F^ 


—     87     — 


99. 


^^^^^^^^^^^^^ 


fe^ 


^ 


-G— 


100. 


p 


1=^ 


3=2s: 


i 


t>— ^> — ^ 


^g 


t=:t 


^ — • — ^ — I — r — I — ^—^- 


t=x 


±I=3t 


-rr 


102. 


^c_,^^ij:jr^j-j+j^j=^^rflf^ 


:^=t 


P^ 


^ •- 


x=x 


f^^ 


t=l 


^s 


W=T 


^§ 


£= 


-i=^c 


P 


?-^S: 


^^^ 


-#« — •- 


fc=|: 


^E^Eg^ 


^P^ 


^EI5^E^-I 


^=:irz=t 


T=^ 


^^m 


The  pupil  is  now  already  capable  of  harmonizing  in  four 
parts  any  folk-songs  which  do  not  modulate,  and  many  cJiorales 
(hymn-tunes,  sacred  choral  songs),  the  melodies  of  which  will 
be  found  in  any  Book  of  Chorales  (that  compiled  by  Erk  is 

very  useful  and  reliable). 


--     88     — 

Thorough-bass  Notation. 

§29. 

The  indication  by  figures  of  intervals,  the  so-called  tho- 
rough-bass notation,  employed  as  a  sort  of  short-hand  for 
determining  the  chords,  was  formerly  in  very  general  use  in 
practical  music,  but  is  now  falling  into  disuse.  It  is,  however, 
of  too  great  importance  for  the  composer  to  be  altogether  passed 
over  here.  Through  this  figure-notation,  the  intervals  which  the 
higher  chord-tones  form  with  the  bass  are  indicated  by  figures 
over  or  under  the  bass  part.  This  renders  it  possible  to  play, 
from  such  a  figured  bass,  a  correct  accompaniment  on  the 
organ  or  piano.  For  the  composer  they  serve  to  indicate  a  chord 
in  a  rapid  sketch  Avithout  having  to  fill  out  the  notes  at  once  in 
all  parts.  The  rules  for  such  notation,  as  far  as  they  concern 
the  chords  already  mastered,  are  the  folio  wins;  : 

Every  chromatic  sign  refers  to  that  interval,  reckoned 
rom  the  bass  note,  before  whose  figure  it  stands;  e.  g.,  the 
sharp  to  the  sixth,  which  is  consequently  cj: 


172. 


A  chromatic  sign  standing  alone  always  refers  to  the  third. 

A  triad,  whether  major,  minor,  or  diminished,  is  not  figured 
at  all.  But  if  its  third  be  raised  in  relation  to  the  signature 
(like  that  of  the  dominant  triad  in  minor),  the  chromatic  sign 
which  would  indicate  such  a  raising  is  written  over  or  under 
the  bass  note. 


173. 


^^: 


§ife 


fl 


-G- 


X=:^ 


I 


In  the  first  example  the  third  is  indicated  by  a  natural, 
because  the  third  of  the  major  dominant  triad  is  &,  not  &[?; 
in  the  second  example  by  a  j(,  because  the  third  is  &J},  not  &. 


—     89     — 


The  chord  of  the  sixth  is  indicated  by  a  6.  Where  the 
sixth  is  raised  as  compared  with  the  signature,  the  correspond- 
ing chromatic  sign  is  set  before  the  6. 


174. 


itei 


-&- 


-(S- 


a 


-.6»- 


:^ 


^ 


The  chord  of  the  sixth-and-fourth  is  indicated  by  |.  Where 
either  of  these  two  intervals  contradicts  the  signature,  the  cor- 
responding chromatic  sign  is  placed  before  the  figure  indicating 
the  interval. 


175. 


m^. 


-zt 


\\    '  jtJ 


^i=^4=^p4 


-<9- 


4==[ 


(9- 


Chords  of  the  seventh,  whether  dominant,  minor,  diminish- 
ed, or  subordinate,  are  indicated  by  a  7. 

The  raised  third  of  the  dominant  chord  in  minor  is  in- 
dicated by  the  corresponding  chromatic  sign  under  the  7. 


176. 


P»^^^ 


-fi^ 


It 


-Kl- 


-&- 


i 


« 


The  chord  of  the  (third),  fifth  and  sixth  (first  inversion 
of  chord  of  the  seventh)  is  indicated  by  \,  Any  chromatic 
sign  required  is  placed  before  the  figure  for  the  interval 
altered.     (In  our  present  exercises  this  concerns  the  6  only). 

The  chord  of  the  third  and  fourth  (and  sixtli)  is  indicated 
by  3.  When  the  chromatic  sign  refers  to  the  sixth,  this  latter 
must  be  added  in  the  notation,  and  the  chromatic  sign  required 
placed  before  it  ;  e.  g.:   tfj. 

3 

The  chord  of  the  second  {fourth  and  sixth)  is  indicated 
by  a  2.  Chromatic  signs  as  above.  Should  a  chromatic  sign 
refer  to  the  fourth,  its  figure,  4,  must  be  added,  with  the  sign 
needed  ;  e.  g.:  S|. 

177. 


mM 


-^—^ 


x=x. 


t=:|: 


\^     I    %%      '  % 


g 


tzzt 


%\  '  %  %  \ 


—     90     — 


178. 

^B. 

— 1 6'- 

-^r 

=Fr 

ff=f=\ 

1 

^^\ 

-^--if-#sp-i 

zf: — ^ 

h^—fH 

\:^=H 

■^ — \— 

A — ^— 

^ 

\ 

I   % 


The  chord  of  the  nintli  is  indicated  by  a  9.  A  chromatic 
sign  standing  alone  under  the  same  refers,  as  elsewhere,  to 
the  third. 


179. 


mm. 


m 


% 


Its  inversions  are  to  be  indicated  by  their  characteristic 
intervals: 

the  first  by  \ ,  the  third  by  | . 


180. 


iii^Sg^ 


:^=t 


-^- 


1^2=^:  z^ 


X=t 


I  I  «  «         I         2         6  g  6  g         I        ^ 

Where  several  chords  occur  over  one  bass  note,  their  figures 
should  be  set  as  nearly  as  possible  in  the  places  which  the 
chords  would  occupy  in  the  measure.  In  such  cases,  triads 
are  also  figured,  and  indicated  by  a  3. 


l«i. 


^ 


» !  ^ !  8  ^ 

4  4 


-^i. 


equals; 


J   I  J   1   I  j_    1 


\Vhere  we  wish  to  show  that  the  higher  parts  hold  the 
same  chord  during  several  notes  in  the  bass,  we  draw  a  line  from 
the  last  valid  figure,  its  length  determining  the  duration  of 
that  chord. 

182. 


^i 


^^=3=f^ 


equals: 


^^p%^ .  i 


^p^ 


p 


^^ 


±zt 


—     91     — 

As  to  the  position  of  the  soprano,  the  figuring  indicates 
nothing;  it  is,  therefore,  left  to  the  insight  already  gained  by 
the  pupil. 

Model  16. 


I 


^ 


h^ 


it^i'iii  i»at*.  -> 


rf^^F^^^m 


as 


^ 


e 


h 


6  9 


^'^#^#^ 


PS 


tpi-r  ^i^n 


¥   %k   <" 


I 


ti*tzJ 


g 


^^^rrVV 


tTT 


gyf"'  r  f-# 


iJJUJ-j 


A 


m 


i=f 


U        6 

^2 


«l 


6         6 
5 


—     92     — 

Exercise  16. 

The  following  figured  basses  are  to  be  harmonized  in 
four  parts,  with  good  vocal  leading  of  soprano,  each  in 
several  keys.  Then  play  them  in  four  parts,  without  using 
the  exercises  already  written.  Finally,  the  basses  of  some 
of  the  examples  for  practice  before  worked  out  (72  to  103) 
are  to  be  figured. 


104. 


Elxamples  for  Practice.     (Basses.) 


m^^^^ 


^^= 


^—P      ^~T 


i^ 


:g;=^ 


-&- 


h      \%l      *     *    2  Si 

105. 


1=^31^^^^ 


8 


e^ 


1=1: 


I 


3^ 


106.  


\     § 


si       "3 


gte^E^Ejg 


\%    Ml 


:«?=l 


l\ 


-^ • 


qi-=^ 


107. 


g    ^S 


W^ 


i^ 


-6*- 


±=t 


-f9- 


^B 


I      «  6  6  6         g  4  6  6 

108.     Poco  allegro. 


SiS 


^ — d — • 


i^ES 


aSEfe^^^fc 


^^^E 


-<5> -, ^T-^ r- 


p^ 


t=T:^:4 


8§    •    8    I    I 


-     93    — 


^ 


t 


-ri- 


^ 


£ 


109. 


\       «^  M2    "81       8  J  J 


w 


^ 


s; 


j^E^ipin^ 


t=!: 


110. 


2 


6        7        2 


;^^ 


gfeeEg^ 


-n — r 


attzm^i 


i-T^ 


g!^jrr^-rrg^^ 


i^st^=3 


E^- 


-4-*-*^ 


i^^fE^E^ 


«»: 


^ 


H^  t|>j      a  • 


8 


«  ^3  \ 


111. 


P5;js^= 


^  sir      ^6  a    6    6      337 


:pT^=f: 


^: 


n 


\      «i 


6         7tj 


S^S^ 


3t=:it 


J^^^t^z^=^ 


81S         t    •  2 


6    2      6 


\l         7 


Herewith  are  ended  the  exercises  of  the  first,  fundamental, 
and|  therefore,  most  important  part  of  the  haimony  course  and 
the  full  course  in  composition.  No  one  should  proceed  to  the 
next-following  part,  who  has  not  attained  complete  mastery 
over  the  material  of  the  first. 


*<H>o* 


•     94     — 


II.  The  Tones  Foreign  to  a  Harmony. 

§  30. 
INTRODUCTION. 

In  nearly  all  exercises  hitherto  worked  out,  the  pupil  was 
obliged  to  use  a  separate  chord  to  each  tone  of  the  melody. 
Such  treatment  would  cause  more  lively  movements  to  appear 
heavy  and  overladen,  and  the  exercises  in  the  first  part  cannot 
be  considered  free  from  this  fault,  although  the  melodies  there 
given  were  calculated  so  far  as  might  be  for  this  style  of 
harmonizing.  We  shall  now  proceed  to  learn  the  conditions, 
under  which  the  accompanying  parts  are  released  from  the 
necessity  of  following  the  melody  throughout  its  progressions^ 
and  the  movement  becomes  lighter  through  a  limitation  in  the 
number  of  the  chords. 

For,  under  these  conditions,  tones  foreign  (not  belonging) 
to  a  chord  may,  nevertheless,  combine  with  the  same. 

Such  tones  are  named,  tones  foreign  to  the  Jiarmony. 
According  to  the  various  conditions  for  their  entrance  they 
are  grouped  in  four  chief  classes:  1.  Passing-notes,  2.  Suspen- 
sions,  3.  Anticipations,   4.  Changing-notes. 

Passing-notes. 

§  31.      ' 

SIMPLE  PASSING-NOTES  IN  ONE  PART. 

A  tone  on  a  relatively  weak  beat,  progressing  by  a  degree 
between  two  harmonic  tones  (i.  e.  :  tones  belongirg  to  a  chord 
—  chord-tones),  is  called  a  Passing-note. 


—    y5    — 


183. 


The  degreewise  progression  may  be  diatonic  or   chromatic, 
but  the  pupil  must  employ  the  latter  very  cautiously. 

Here  the  chromatic  signs  have  no  influence  on  the  key. 


^ 


=f 


<9- 


I 


In  triple  (ternary)  time  the  passing-note  may  occur  on  the 
second  or  third  beat  or  subdivision,  i.  e.:not  necessarily  be- 
tween two  strong  beats. 


185. 


I 


I 


t 

3 


^^^fe^^^a 


F=^ 


^=^ 


The  progression  is  directed  either  upward,  or  downward, 
or  backward  (i.  e.:  leading  back  to  the  preceding  tone). 

186.  .  ,  .  ,  .       ,         . 


m. 


^ 


■y^ 


3^ 


•^1 


-G- 


r^— 


is: 


# 


-&- 


-©'- 


f 


The  first  two  progressions  usually  require  in  minor,  with 
\he  corresponding  leadings,  the  melodic  form  of  the  scale. 
(Elements  of  Harmony  and  Notation,  §§  45,  46). 


187. 


m. 


G^ 


m 


m 


—     9fi 


Faulty  progressions  of  chord-tones  are  not  neutralized  by 


passing-notes 

I       ,       ,   equals 


188.  a 

Si 


m 


^U- 


5b 


eqaals 


U 


p 


:^' 


-,*—"♦ 


-<9- 


I       ■  r 

By  the  passing-note  f  (fourth)  the  parallel  fifths  at  a  are 
not  neutralized,  because  the  intervals  on  the  strong  beat  im- 
press themselves  on  the  ear  as  essential,  and  the  ill  effect  of 
the  parallel  fifths  on  the  strong  beats  remains  quite  as  sensible 
as  without  the  passing-note.  The  same  is  true  of  the  parallel 
octaves  at  b.  Single  passing-notes  on  weak  beats  cannot  form 
false  progressions. 


I      I 


189. 


-^=^- 


Ml 


^- 


Preparatory  Piano-exercise.  Strike  chords  with  the  left 
hand,  and  play  to  them  with  the  right  hand  a  part  containing 
passing-notes.  Play  cadences  with  passing-notes  in  the  bass; 
first  with  two,  secondly  with  three,  thirdly  with  four  notes 
in  the  bass. 

Exercise  17. 

Given,  an  harmonic  movement  in  the  form  of  a  figured 
bass.  (I)  The  soprano  of  same  is  to  be  changed  to  a 
continuous  flow  of  quarter-notes,  and  wherever  possible  by 
means  of  interpolated  passing-notes.  Bass  remains  un- 
changed ;  the  other  parts  sustain  the  given  harmony.  (2)  Now 
treat  the  alto  as  the  soprano  was  treated.  Bass  unchanged  ,- 
soprano  and  tenor  sustain  harmony.  (3)  Tenor  like  alto 
above.  Bass  unchanged  ;  soprano  and  alto  sustain  harmony. 
(4)  The  bass  itself  is  to  be  changed  to  a  flow  of  quarter-notes. 
The  other  parts  sustain  harmony. 

Each  of  these  exercises  should  be  written  out  several  times 
to  one  harmonic  foundation.  First  write  out  the  bass  part; 
then  the  part  in  quarter-notes,  with  regard  to  its  own  position 
and  to  that  of  the  parts  still  left  out,  and  to  the  given  harmony. 


—     97     - 


The  employment  of  passing-notes,  and  of  other  foreign 
tones  to  be  treated  of  later,  sometimes  necessitates  a  doubling 
of  even  those  dissonant  intervals,  whose  doubling  was  hitherto 
not  allowed.     In  these  examples: 


190 


i 


m 


i 


i 


4: 


9i 


r-p- 


^ 


m^m 


the  seventh  in  the  chord  of  the  seventh  may  properly  be  doub- 
led in  passing  (provided  that  the  foregoing  movement  in  the 
parts  was  similar,  and  in  order  not  to  interrupt  the  same), 
because  the  further  leading  of  the  soprano  insures  us  against 
false  harmonic  progressions.  On  the  contrary,  such  a  doubling 
would  be  blamable  in  the  following  example: 


191. 


P^ 


:^= 


"m- 


For  here  the  strong  beats  show  parallel  octaves  between 
soprano  and  tenor,  and  the  minor  third  interpolated  on  the 
weak  beat  in  the  soprano  is  not  prominent  enough  to  neu- 
tralize the  effect  of  these  octaves.* 

Model  17. 


Given.                                                                    ill 

6 


*   Kespecting  manner  of  writing  the  half-notes  compare  Elements 
of  Harmony  and  Notation,  §  33. 

B ussier,  Elemantary  Harmony.  7 


98     — 


b^ 


i 


i 


tj: 


9^ 


-1^ 


HSL 


2Z 


J 


N^^H^rM^^^r^Wf 


6>- 


^^^ 1^ 


J       J     ,J 


9i=a: 


—     99 


N.B. 


IS 


1 


iiij  j  Jiai  iJJi  jiJj 

/  rj  —  --<g — h- 


I 


1 


:©: 


i 


i 


^- 


i 


s 


^e 


I 


-f^- 


-19- 


f 


Iffil 


:£ 


«n»:r— y 


^m 


is: 


7* 


—     100    — 


N.  B.  Here  the  third  of  the  dominant  chord  could  be 
doubled  in  passing,  (1)  because  parallel  octaves  neither  result 
therefrom  nor  can  even  be  presupposed,  for  the  skipping  pro- 
gression of  the  soprano  is  required  by  its  leading  in  the  very 
first  four  measures;  (2)  because  the  weak  beat,  together  with 
the  smooth  leading  of  both  the  lower  parts,  while  the  higher 
parts  are  sustained,  prevent  the  doubling  from  being  prominent ; 
(3)  because  any  other  leading  of  the  parts  woald  be  more 
awkward. 

Examples  for  Practice. 
The    inner    parts    are    not    bound    to    tlie    rliytlim    of    the 
bass.     As   a  substitute   for   an   indicated   chord,   some   other 
chord  may  occasionally  be  taken,  that  can  fill  its  place. 
112. 


gS^E^t 


i^ 


si=t 


.(^1 


\ 


113. 


g>— 


-?5^ 


^S 


75^ 


114. 


Si^s^i 


&—^ 


g^ 


&-^ 


115. 

H^^M — 

1 1 

1      ^. 

r  ^   f 
1         iTj* 

i    Ji 

Jj 

R=^^-^ 

2 

—*y- — h — 

6          6 

^¥^=^ 

6         6 

2       6            6 

116. 


^^la^^i 


^ 


^^ES 


1 


&-^r-^ 


117 


&- 


^^11 


B: 


1^ 


t^ 


TS*- 


IZIZ^TI  -fi^— 6,-  ^-=^ 


«  6  9    6    9    7 


\h    '       5 »   J 


101  •^- 


Harmonize  the  following  m^odles,  noftta?R?ng  passing- 
notes,  in  four  parts. 

Model  17  a. 


l^SS^^fe 


^dj=azs 


■  'v 

n 


^^ 


E^rS: 


f- 


\S 


-- , 


^^«fi 


U 


r 

J 


f 


e^fe^ 


i 


^^^EEfelf 


II  I 


-ti^ 


118. 


Examples  for  Practice. 


=zzz:V:q=j: 


^i^s 


^^EgErE 


istj: 


119. 


^S 


:£:* 


S 


lissiut 


ziiwiz^W 


EE^ 


j;    ^         120. 


u 


IW^^^^^^^^^^^I 


—    102     — 
121. 


e^ 


1=1: 


^^ 


SS 


ifzit 


=]: 


-j i-«d 


-m—^ 


U 


^^^^^^^^g^a 


i 


fci: 


^ 


l'=i=l'=»=S^ 


122. 


r^^^ 


lilatd 


fm 


1. 


^fc^=g^ 


E«^ 


S^ 


# 


r: 


IS 


?^=f: 


l^EE 


§  32. 

SIMPLE  PASSING-NOTES  IN  SEVERAL  PARTS. 

Passing-notes  may  also  enter  simultaneously  in  two  parts, 
provided  that  they  cause  no  faulty,  ill-sounding,  or  unnatural 

progressions  or  harmonies  ;  whence  it  follows,  that  their  progres- 
sion in  thirds  and  sixths  is  preferable  : 


192.    < 


m- 


i=i=hj-i-:-. 


rrr^-m 


J. 


^ 


*-^ 


i 


-£^ 


193.  ^ 


r 

I     i 


as£ 


U^M^^^A. 


—     103 


Occasion  may  sometimes  offer  for  writing  three  simul- 
taneous passing-notes.  And  in  general  it  is  possible,  in  poly- 
phonic writing,  to  admit  a  number  of  simultaneous  passing- 
notes  less  by  one  than  the  entire  number  of  parts.  (Model  18, 
measures  7  and  15). 

Exercise  18. 

Work  out  the  following  basses  and  sopranos  in  four 
parts,  employing  practically  the  suggestions  in  this  §.         -h^iP^f) 


Melody  given. 


Model  18. 


I 


a 


^-f 


^=^ 


-m 


J- 


rrt 


j=i 


^ 


^ 


9fc# 


4r-^ 


i         ^ii  A 


^ 


r 


r  rlf^rm 


W'^i^r 


Hi — ^ 


i 1   _il 


r^rr^ 


i 


[•'•  '/•  - 


1  ii  i- 


e 


p 


Bass  given. 


^wir^-^i^=^- 


¥ 


te 


J^ — i 


^ 


15^ 


f    1^    r 


—     104     — 


\m 


^h#=^^tN 


F=^^ 


^1A±U  iii 


G^ 


t 


123. 


Examples  for  Practice. 


^^ 


:s=t 


9— ft 


^^^^"^^ 


^^    6    6    6  ^  f  I     f        I  1^      ^ 

»  I    I    I    r    '    I 


'  '  '  ■  '  ill  I 


^^^i^^^^p^^ 


^^^^ 


P-m- 


=^^ 


^^^^ 


izS, 


^ 


-§i^^ 


frt 


126. 


•^ 


■t=5: 


§^P^ 


^ 


m 


lr=± 


8 • 


.^i- 


—     105     — 


§  33. 
COMPLEX  PASSING-NOTES. 

Two  or  more  foreign  tones  progressing  by  degrees  may 
likewise  occur,  on  relatively  weak  beats,  between  two  chord- 
tones,  and  thus  form  double  or  complex  passing-notes. 

In  triple  time,  such  passing-notes  may  also  occur  between 
the  first  and  third,  or  between  the  second  and  (the  following) 
first  beats  or  subdivisions  of  the  measure.    (§  31,  No.  185.) 


194. 


M 


^p^pi^ip^^^ 


-<s>-' 


J. 


i 


St 


1 


I^"^ 


i^=^       l-HP^"       \—¥^^ — l~~Th 


P 


Exercise  19. 

Work  out  the  following  melodies,  containing  such  pas- 
sing-notes, in  four  parts. 


I 


s 


Model  19. 


^^ 


:^ 


^ 


J. 


^S. 


t 


—     106     — 


I 


s 


^ 


I        ^      J 

0* — G* 


^^ 


i-  J' 


t 


9#=? 


■f^t 


P 


^  r  i-p^^ 


^ 


J:    i    1.      i2imi. 


5 


£ 


t 


127. 


Examples  for  Practice. 


^^^^^^^^^^^^ 


^^^^^^^ 


^^^3^33^3 


—     107     — 


128. 


t 


^ 


Si 


^^^^^^ 


T=^=r=f=f 


$ 


rf  i'^ 


129. 

i 


is 


m 


91* 


-^^^ 


gg^^T^=g=g^^^fe^^^^^^ 


1^ 


F^#- 


^^^i^^gl 


but 
and 
195, 


§  34. 

PASSING-NOTES  ON  WEAK  BEATS.   INOOERECT 

CHANGING-NOTE? 
Tones  which  fulfil  all  other  conditions  of  passing-notes, 
occur  on  a  strong  beat,   are  reckoned  as  passing-notes, 
treated  as  such. 


I 


I      I 


• — 1^ 


i 


Ui 


'^m 


trrjf* 


P 


r-^rrf 


^ 


As  they  exchange  the  weak  for  the  strong  beat,  they  are 
sometimes  called  changing -notes,  but  improperly  so,  because 
the  original  sense  of  this  term  has  reference  to  an  alternation 
between  a  consonance  and  a  dissonance.  Properly  speaking, 
they  are  suspensions  introduced  by  a  degree. 


—     108 


The  tone  preceding  such  a  changing-note  is  either  a  chord- 
tone,  or  a  common  passing-note;  in  the  latter  case,  therefore, 
we  have  a  passing-note  and  a  changing-note  in  succession. 


196. 


Wz 


I  "'I 


Ch. 


P.   Ch. 


^i 


J— J— J-: 


^i 


i 


^E 


I 

i- 


P.  Ch. 

In  cases  evidently  originating  with  double  passing-notes  the 
changing-note  may  be  followed  degreewise  by  a  passing-note.  E.g. : 


197. 


I 


is  admissible,   because  it  can  be  shown  to  originate  with  a 
regular  double  passing-note  (§  33). 


198. 


^m 


The  entrance  of  such  tones  is  restricted  solely  by  the  rule, 
that  they  must  not  form,  with  the  tone  to  which  they  progress, 
the  second  of  the  same  octave.  Consequently,  the  following 
leadings  are  strictly  regular. 


199. 


—     109     « 

Exercise  20. 

Work  out  the  following  examples  for  practice  in  four 
parts,  in  such  a  form  that  the  added  parts  shall,  in  general, 
progress  in  notes  of  greater  value  than  those  of  the  given 
part.  E.  g. :  when  the  latter  is  in  eighth-notes,  write  the  others 
in  quarters,  halves,  or  even  whole  notes  ;  if  in  quarter-notes,  take 
half  and  whole  notes  ;  in  triple  time,  dotted  notes  of  greater 
value  may  be  employed. 


Model  20. 


i- 


^^^§^^m 


m 


J 


i 


I 


I 


^ 


15" 


f— r 


Examples  for  Practice. 


t=.\. 


±zX 


-^-=\^ 


=t=)=: 


t=±l 


—     110     — 


^^^^^fej^ 


^££s 


^§ 


I 


■^ 


^=E 


^^EE 


^:Srft:jj^=^ 


^^^fefe^^^^^ra 


132.  ^^ 


^'- 


M 


gfe^:zjz£C:L^^|^r?fr^^ 


T:F 


#-#- 


133. 


^ 


^^8t=^ 


g 


W=^—F 


$^$ip 


:p=t==t 


l=:t 


4fc     »  1"7Si:T| 


134. 


SiE^^E 


^^E 


t=t 


^^m 


v^^^ 


^w^»- 


X^=».=^. 


VI 


4-J 


S^^ 


!1^£±JE^E^ 


-j — w—\- — I ! F- 


s^ 


^^E53 


i 


3^ 


VI 

135^ 


?Ei 


II  V  I 


^^^^iS 


a 


■•-#■ 


itt 


^P 


^  136. 


|g^^pzj,j  J  Lj_jff^W:^r3^F-^ 


a«^^^^Ep^^^qa=r]=^3E3Eg^ 


— .   Ill   — 


137. 


m^^E^^^^ 


agE^^:^ 


^S^g^^^^^^ 


g^^^^^ 


==££=:■ 


^^^^^m^^^m^ 


The  Suspensions. 

§B5. 

TIED  SUSPENSIONS. 

The  Suspension  (suspended  tone)  occupies  a  relatively 
strong  beat  or  subdivision,  and  resolves  to  a  chord-tone  on  a 
relatively  weak  beat  or  subdivision,  the  chord  itself  being*  held 
unchanged  in  the  other  parts.  A  tied  suspension  is  a  tone 
which  was  a  chord -tone  in  the  chord  immediately  preceding, 
and  in  the  same  part.  In  triple  time  the  second  beat  (or  sub- 
division) is  considered  as  strong  in  comparison  as  the  third  (comp. 
chord  of  the  %,  §  13). 


200. 


N 


-X- 

I 


^^z^_ 


-•—^ 


(9 


~G- 


g!EB=^f=^ 


f 


(9- 


P 


^ 


i 


^ 


^ 


^ 


^^^m 


^ 


:?i==t 


112 


For  the  treatment  of  tied  suspensions,  three  rules  have,  there- 
fore, to  be  observed  : 

(1)  The  entrance  of  the  tone,  later  suspended,  as  a  chord- 
tone  in  the  preceding  chord  —  the  preparation; 

(2)  The  suspension  itself,  which  forms  a  dissonance  with 
the  accompiinying  chord; 

(3)  The  resolution^  by  a  step  downward,  to  the  chord-tone, 

/    \  Prepa-     Sus-      Reso- /v  \  Prepa-     Sus-  Prepar.     Sus-  Prepar.     Sus«    Reso- 
V   /   ration,     pens,     lution.v'-'/ ration,    pens.   Resol.      pens.   Resol.     pens,  lution. 


201. 


-25'- 


-&- 


^: 


z^: 


1 


etc. 


g^E^ 


_«CrL 


G- 


I 


At  (a)  are  exhibited  the  three  elements  of  a  tied  suspen- 
sion; at  (h)  a  succession  of  suspensions,  wherein  the  resolution 
of  the  one  serves  also  as  a  preparation  of  the  next. 

For  the  relation  in  which  the  preparation  stands  to  the 
suspension,  observe  the 

R  TILE :  The  preparation  must  not  be  effected  by  a  note  of 
shorter  value  than  the  suspended  tone  ;  i.  e. :  a  long  note  must 
not  be  tied  to  a  shorter  one.     E.  g. : 

not  J  I  J,  not  J  I   J^,  not^^l^J  eta 

For  the  relation  of  the  suspension  to  the  accompanying 
chord,  observe  the 

BULE:  The  suspension,  and  the  chord-tone  to  which  it 
must  be  resolved,  must  not  meet  each  other,  in  the  same  octave 
and  different  parts,  in  the  interval  of  a  second. 


204. 


Consequently 
not: 


EE?i 


:j- 


l^-^^l 


-^- 


gfce 


-fid- 


-Ci- 


—     113 


A  meeting  of  the  suspension,  and  the  chord-tone  to  which 
it  resolves,  in  the  unison,  even  in  different  octaves,  should,  when 
feasible,  be  avoided;  i.  e.:  where  neither  the  leading  of  the 
parts  nor  the  fullness  of  the  harmony  suffers  thereby.  For 
instance,  we  should  avoid: 


203. 


z^ 


i 


--^=^ 


^^m 


J  I,  J-rJ  J 


r 


«: 


^ 


-P- 


1 


fe 


and  give  preference  to: 


-ci- 


i-=i 


-6»- 


m^ 


J— rr-'^^^^r^     J 


e^- 


9l^ 


^; 


i 


Similar  cases  may,  however,  appear  quite  justifiable  in 
consideration  of  good  leading  or  full  harmony,  and  are  best  in- 
troduced by  contrary  motion;  e.  g. ; 


204 


1^^ 


'G 


^1 


-fU. 


■^ 


:^ 


^^ 


-r:t 


J 


? 


a- 


r- 

But  the  leading -note  (seventh  of  the  key,  appearing  as 
such  as  third  in  the  chords  of  the  dominant  and  ninth,  and 
as  fundamental  in  the  diminished  triad,  and  minor  and  dimin- 
ished chord  of  the  seventh)  must  never,  ivhile  entering  in  one 
part,  he  retarded  hy  suspension  in  another* 

Bussler,  Elementary  Harmony.  8 


—     114     — 


205. 


Never : 


■tl 


1 


:i» 


s — ^- 


m=\ 


False  progressions  are  not  neutralized  by  suspensions,  al- 
though the  suspension  is  far  more  prominent  than  the  passing- 
note.  With  suspensions,  parallel  fifths  and  octaves  on  weak 
beats  must  be  avoided. 


/z- 


2^=; 


-&- 


-G- 


IQL 


206. 


I  equals: 


^^- 


^ 


i 


-irt 


=f. 


3s: 


^^- 


At  first,  we  shall  employ  the  suspension  only  m  the  soprano, 
as  its  entrance  in  the  bass  or  inner  parts  necessitates  modifications 
of  the  directions  given. 


Exercise  21. 

Work  out  the  following  figured  basses  in  four  parts, 
with  as  numerous  suspensions  in  soprano  as  possible. 

The  figuring  refers  only  to  the  chords,  not  to  the  sus- 
pensions. 

Model  21. 


tf     VV- 


^ 


^—± 


Si- 


Zi^=±=± 


^ 


r  r 


r 


4 


r  r 


? 


&- 


4 


115 


I^EJSEJg 


9* 


r 


<5> 


-G- 


rs 


r 


.: 


.C2. 


1 


138. 


Examples  for  Practice. 


"ms^m 


G- 


w 


ESE?: 


-f9T-f2 


i^mm 


^~^1  h  ^  r^  t  ^i  ^^  (E)  2  J 


139. 


ISSfeeE^t 


£Eti:EEt:: 


=^=^ 


Hii'- 


I^ 


:=l=q: 


2         0 


^r  6       6  6       7 


140. 


is^E^i 


-fi>-T 


^^=^ 


te 


6         6 


S   flt 


6^ 

tl 

6     be 
1 


It 


£ 


6         0 


i^mi 


141. 


gj^^-i^g 


-<5>- 


-^—^-r 


4:=t: 


'    i 


6         6       2         8       7 


Exercise  22. 

Work  out  the  following  melodies,  containing  tied  sus- 
pensions, in  four  parts,  but  without  suspensions  in  the 
lower  parts. 


Model  8. 


i 


.b 


-# — #- 


^ 


J-     J  J  J 


.Ql 


■^ 


G 


^, 


i 


8* 


-     116 


*—G 


^ 


^ 


r^ 


^^fe 


^^XJ.J_J 


a!|-=f^^q^=^ 


142. 


Examples  for  Practice. 


B^fr-r:ig_»j!=M: 


#— I — •- 


=p-«- 


i-fe- 


fi^F^=^=^?^^3^7n:lzg 


:p==i=p: 


U: 


i^f=t=^ 


ffli^s^ 


143.    Adagio, 


^f=*-#^ 


^P=^ 


fr-^=^ 


t=t: 


^^-# 


1:1= 


144. 


H-^ 


3^^ 


^ 


fcti^fi^t 


fc4i=:=lz 


i 


•    p  T""yT 


:^ 


^ 


^=q: 


-^ 


»t=i^^ 


t=tx 


i 


i 


145. 


^^^ 


=F=^ 


r=::=l 


i=t 


:^ 


^2 m — 


1 — r 


^ — r 


I^P^: 


ifciza: 


*  Here  the*  suspension  falls  on  the  dot. 
**  Suspension  on  second  beat. 


—     117     — 


§  36. 

TIED  SUSPENSIONS  IN  BASS. 

For  suspensions  in  the  bass,  the  rule  concerning  the  re- 
lation of  suspension  to  harmony  (given  in  preceding  §)  holds 
good  unconditionally;  i.  e.:the  suspension,  and  the  chord-tone 
to  which  it  resolves,  must  not  meet  in  unison,  either  in  the 
same  octave  or  in  different  ones.    Thus  the  following  cases  are 


inadmissible: 


^=g^- 


gi 


^ 


-<9— ?b 


1=t 


:t=ptzz 


Exercise  23. 

Write  the  higher  parts  to  the  following  basses  con- 
taining suspensions. 

Model  23. 


0m. 


G- 


15h 


i 


EgP¥f^F 


J 


^.   J   J       J  i 


itt^lEjg 


(•g^ 


t 


f  r 


-(^- 


—      118     — 


146. 


PgpBE^^^ 


Examples  for  Practice. 


147. 


i^^ 


^— ^-i 


Egg^-.gE|^W_eE^-gSp3^E^ 


P^^^^^^-r^E^ggglg^J^^^ 


r*"  1       f — i w~ 

148. 

r^»^  f    *  1 

=9^pr-^=f— .•^=r= 

-&— 

^-R=J=f--»-P 

Id — ^ 1/ 

^  li                 1 L_. 

—J — u  ' 

9^ 

— /— 

HiZ 

-p-rT — *- 

-T~ 

_-^. 

1=:^— •:: 

*- 

=^ 

^ 

r  f  |_ — w 

V- 

=t= 

_?_•_;_ 

=3—^ 

4^ 

-•=^ 

-^^— *— r— ^— ^-t-t^— r— ^— r 


:9 


§37. 

TIED    SUSPENSIONS  IN   INNER   PARTS. 

Suspensions  in  an  inner  part  stand  in  like  relation  to  each 
liigher  part  as  does  the  suspension  in  the  bass  ;  to  each  lotver 
part,  as  the  suspension  in  soprano.  Thus,  if  a  suspension  enter 
in  an  inner  part,  a  meeting  of  the  same  with  that  chord-tone,  to 
which  it  resolves,  is  permitted  in  a  different  octave  when  the  sus» 
pension  lies  above  said  chord-tone  ;  as  here  : 


208. 


Correct : 


f 


11^: 


•^fc 


:g: 


<i.       ^ 


—     119     — 

But  such  a  meeting  is  inadmissible,  when  the  suspension 
lies  below  the  chord-tone  to  which  it  resolves,  as  here: 


209. 


Incorrect : 


The  rule  concerning  the  relation  of  the  tied  suspension  to 
the  chord-tone,  therefore,,  can  be  stated  in  more  general  terms  : 

An  anticipation  of  the  suspension  by  the  chord-tone,  to  which 
it  resolves,  in  the  second  of  the  same  octave,  is  always  inad- 
missiUe.  Such  a  meeting  in  different  octaves  is  admissible  when 
the  suspension  lies  in  a  higher  part ;  and  inadmissible  when  it 
lies  in  a  lower  part. 


Exercise  24. 

Work  out  the  following  melodies  and  basses  with  reg- 
ularly tied  suspensions  brought  in,  now  In  one,  and  now 
in  another,  of  the  added  parts.  Where  a  suspension  is  im- 
practicable, try  at  least  to  make  up  for  it  by  a  tied  (syn- 
copated) note. 

t  I 


210. 


I 


^^r 


f 


i^ 


is: 


f 


In  any  case  see  to  it,  that  the  move- 
ment is  kept  up  on  the  weak  beats;  be- 
cause a  sudden  halt  for  the  length  of  a 
half- measure  would  have  the  effect  of  a 
break. 


m 


r 


-i.  d 


Wi 


—     120     — 


Model  24. 

I 


I 


^^^iS 


G G 


r-rf 


1^ 


m. 


4- 


i^iiiJ.   J  J, 

-'- — H^- "^r~i  Q      ,   i-(g^ 


J- 


^^ 


^f^ 


G ^ 


i 


G 


i 


-G 


i 


■P 6^ 


e 


J. 


149. 


Examples  for  Practice. 


@^ 


I 


3: 


<5*- 


f^-<^ 


150. 


=e^ 


:1=^ 


-^^=-0- 


q=:^ 


151. 


35^Ee^ 


6*— H^ 


t^t=[: 


n     g- 


ata:^ 


* 


r^ 


IS 


M  i*  152. 

0fm 


1 — I— Fr 


-f^-^G- 


t^^=?^ 


m 


153. 


T5^— «5>- 


—     121     ^ 


« 


f^-& 


:[=t 


154 


^j^^^E^-^l^gE^ 


^zz^ 


§38. 

SUSPENSIONS  IN  TWO  PARTS. 

Simultaneous  suspensions  in  two  parts  are  prepared  and 
resolved  like  simple  ones. 

211.  I  I  F^ 

N     J.        f^ 


i 


nt 


-•— 


'^^^w-rf^p^ 


-^ 


^ttf^ 


p^ 


S^fS 


f 


r— r 


?^ 


•^r^E 


4=- 


-C 


Exercise  35. 

Work  out  the  following  melodies  in  four  parts,  employ- 
ing two-part  suspensions. 

Model  25. 


^^^^ 


i^ 


^ 


-(2 H-l*- 


p 


^ 


r 


^1 


155. 


—     122     — 
Examples  for  Practice. 


't^^3^^^^^^^^^ 


■±i=Mi 


-P— 6»- 


156.     Comp.  143. 


§s^i^^^g^ 


m 


^^:^^. 


157. 


t=-l 


±Z^. 


SEE 


^.=f=^ 


^:,li=izj=^= 


l=ri: 


3^? 


:^^^§ 


158. 


§£^"4^ 


-^- 


3^i 


^^ 


33f 


t=:l 


Harmonize  descending  major  scales,  and  cadences,  with 
suspensions. 

§  39. 

RETARDED  RESOLUTION  OF  TIED  SUSPENSIONS. 

The  regular  resolution  of  a  suspension  may  be  retarded 
by  an  interpolated  tone  belonging  to  the  accompanying  chord. 


212. 


m 


'^M 


m 


-G^ 


-fSi^J 


-^ 


The  skip  of  a  fifth  downward  {ci)  exhibits  much  the  com- 
monest form  of  tliis  retardation,  through  which,  as  may  be  seen 
here,  the  tying  of  a  long  note  to  a  shorter  one  is  avoided. 


—     123     — 
The  interpolated  tone  may  also  enter  by  a  skip  upward. 


213. 


^3Et^^^ 


r=r 


^t 


-^J 


f^ 


S^^l 


Exercise  26. 

Work  out  the  following  melodies  containing  such  re- 
tardations. 

:^.   Model  26. 

J-JcJ 


atti 


^f^f^Xr'T^? 


I— J: 


;i-i^i^ 


j: 


9ir3 


#— it 


?: 


4r 


F 


1^ 


I 


J 


5 


^ 


15^ 


r 


-&^ 


^ 


X 


J, 


r 


9 


•  ^^* 


159. 


Examples  for  Practice. 


'^ 


EE^; 


-^ 


-&* 1— »=p: 


It  160. 


ilO: 


—     124 


^ 


■ti 


&- 


gtE^EE^^S 


161. 


^t=x 


S5 


-^ 


t=:t: 


§40. 

SUSPENSIONS  FROM  BELOW.  —  SUSPENSIONS  IN 
SEVERAL  PARTS. 

All  suspensions  till  now  employed  were  resolved  down- 
ward; and  this  is  by  far  the  commonest  resolution.  But,  from 
the  leading  of  the  parts  or  the  character  of  the  melody,  sus- 
pensions may  result,  which  require  an  upward  resolution.  In 
musical  terminology  the  suspensions  already  treated  of  are 
called  suspensio7is  from  above ^  because  they  progress  from 
above  downward.  On  the  other  hand,  suspensions  which 
resolve  upward,  thus  exhibiting  the  reverse  progression,  are 
called  suspensions  from  heloiv.  They  occur  chiefly  when  some 
tone,  by  reason  of  its  affinities  in  the  key,  has  a  tendency  to 
progress  upward;  e.  g.tthe  seventh  (leading-note)  of  the  scale. 


214. 


Any  other  tone  of  the  key  can,  however,  be  endowed  by 
the  melody  with  this  tendency  to  resolve  upward;  e.  g.;in  the 
following  case,  which  receives  its  first  impulse  from  the  seventh. 


Prepa-     Sob-  Prepar.  Sns- 
ration.    pens.  Resol.  pens. 


215. 


I 


^ 


^. 


-^1 


T 


I      I 


r 


5fc 


3 


I 


--zz^ 


-#- 


—     125 


Suspensions  from  below  and  above  may  be  combined  in 
two-part  suspensions. 


With  retardation. 


216. 


Suspensions  in  several  parts  at  once  are  usually  combi- 
nations of  suspensions  from  below  and  above;  but  tbey  may 
belong  to  only  one  of  these  two  classes. 

In  the  resolution  of  polyphonio  suspensions,  either  each 
single  suspension  is  resolved  regularly  downward  or  upward, 
or  else  all  of  them  together  are  conceived  as  one  suspended 
chord,  and  treated  according  to  the  rules  governing  chord- 
progression. 

(a)        ,  .  I  j(h)_j_ 


817. 


^^ 


-G- 


S^ 


^    J l(^)    |_     |(d)   ._     I         ,  (e)    I 


Z3L 


(a)  Here  the  second  part^  as  third  of  the  dominant  chord, 
takes  advantage  of  its  liberty  to  progress  by  a  skip,  and  is 
therefore,  treated  as  a  chord-tone,  not  as  a  suspension. 

(b)  Here  all  tones,  whether  as  elements  of  the  chord  of 
the  ninth  (minor  chord  of  the  seventh),  or  as  suspensions  from 
below  or  above,  are  resolved  regularly. 

(c)  Here  the  c  of  the  alto,  as  a  chord-tone  to  the  bass  f, 
progresses  freely  by  the  skip    of  a   third;   the  suspension  is, 
therefore,  only  in  two  parts. 


—     126     — 


(d)  Here  all  parts,  whether  as  single  suspensions  or  as 
elements  of  suspended  chords,  are  regularly  resolved. 

(e)  Here  all  suspensions  resolve  upward,  and,  as  elements 
of  the  chord,  are  likewise  ti-eated  regularly. 

Some  of  these  forms  of  progression  have  even  received  spe- 
cial names  (hardly  used  in  English)  as  chords;  thus,  for  example, 

The  tonic  with  suspended  chord  of  the  seventh  (or  dimin- 

218.  prg=g^ 
ished  triad),  called  chord  of  the  11th.  F=g — ^~\ 

The  tonicwith  suspended  chord  of  the  ninth  (or  minor  [diminish- 

219.      ^_f:_^ 
ed]  chord  of  the  seventh),  called  chord  of  the  13  th.  p=g— ^^=^=1 

The  so-called  chord  of  the  fourth  and  fifth  is  a  triad  with 

220.  r-^       jj 

suspended  fourth.  EsE^iizd 

4 

Exercise  27. 

Harmonize  the  following  melodies,  employing  suspen- 
sions from  below  and  suspensions  in  several  parts. 

Model  27. 


^T-f='f-ff 


i=t 


Wfi^* 


rrri- 


jj. 


iJ-  JJ  ii 


^ 


g%j£pi^g^ 


^ — 


I 


4^ 


i+^ 


^ 


•^=^ 


I 


-^ — (^ 


s 


rp 


1 


162. 


=3^^E 


^     127      — 
Examples  for  Practice 


•^+;f=p: 


SE^^ 


\-f=x 


^t 


:'^E 


1==^- 


X:=^=t 


|f:iiff 


« — • 


1i=i=:: 


F2=Er=*'^E5 


163.^ 


^i^^^^l^^ 


li^^l^^i^^^^^ 


;^^^^^P^f^=F"'^|: 


-fe- 


-^T^- 


^^ 


35EI^ 


I 


To  the  tied  suspensions  are  also  reckoned  those  preceded 
by  the  same  tone  in  the  same  part  even  witliout  a  tie.  In  these, 
the  preparing  tone  may  be  shorter  than  the  suspended  one. 


221. 


i 


4.P^ 


^S 


J   J   I 


i 


j- 


5;=t 


:g: 


r  T 


r  "  * 


I  I 


Si 


q: 


tip: 


itit 


Suspensions  of  this   class  are  contained  in  the  following 
melodies  belonging  to  Exercise  26. 

164.  +  t  +  t 


^^m^^m^m 


m 


:h: 


^^m 


t^ 


*  Lower  parts  pause  for  this  Auftakt  (fractional  opening  measure.) 


—     128     — 


166. 


S 


t==t 


^8,--i^TJte^ 


3^HE^ 


t==[: 


:^ 


:ir=p: 


i 


s 


^ 


Si;^^ 


— <&- 


§41. 
FREE,  OR  QUITE  UNPREPARED,  SUSPENSIONS. 

Free  suspensions  are  foreign  tones  entering,  without  prep- 
aration,   on     strong    or    weak    beats,    and    resolving    regularly 

upward  or  downward.    They  may  embrace  one,  two,  or  more 

parts. 
222. 


^i^3^- 


I    ^   «^  i^  J  J    I  J  I   I    I  T-n 


Ifce 


r-i^ 


I     I 


f— f 


I       i 


^- 


^^m 


m^^^m^ 


^^,=t 


^ 


^ 


H»— 


a^ 


6» 


^^^^^^^ 


m 


J/ 


:^ 


-  -        8    F 


^11=^ 


—     129 


The  sole  restriction  for  these  suspensions  is,  that  the  sus- 
pension, and  the  chord-tone  retarded  by  it,  shall  not  meet  as 
a  second  in  the  same  octave.     Thus: 
223    wrong:  but  right: 


f^^ 


W 


5^ 


-m-±-'i*f9 


5t^= 


^rn'=f 


Exercise  28. 
Work  out  the  following  melodies  in  four  parts. 

Model  28. 


pB^ 


±=^ 


•— *H 


m^f^m 


5« 


rr 


SEtE 


r 


-^- 


r  r 


e 


P 


s 


f 


# St 


'-P^^^^ 


IB 


e 


^ 


f 


— f-'t— r 

Examples  for  Practice, 
167.    Adagio. 


^ii 


-jiq- 


#-»-r-» 


!isr^^^s^^^g 


Bussler,  Elementary  Harmony. 


—     130     — 


t^ 


^^ 


^i^ 


168. 


^ 


m^^^ 


^=? 


5i=P=^ 


-^— »- 


P^^ 


i 


^ 


i^n 


:i==*=^: 


^ 


J^T- 


^^^eS 


F— • 


ipzzii 


-•-- 


-\- 


^— •- 


:t=^ 


:^ ^ 


u  ^  JA  it   170. 


£ 


^-9 


m 


^^^ 


i^^ 


:p=^ 


^§is^ 


§  42. 

ANTICIPATION. 

Tones,  wMch  enter  one  chord  as  foreign,  and  in  the  next 
chord  and  same  part  become  chord-tones  by  means  of  ties  or 
repetition,  are  called  anticipations;  because,  while  properly 
belonging  to  the  second  chord,  they  are  already  anticipated  in 
the  first. 

t 

I 


224.  A        I       I        I        I  ^j I      I 


r 


i^zi: 


-G- 


~o- 


^m 


-     131     — 


Anticipations  are  rarer  than  passing-notes  or  suspensions. 

We  also  class  with  the  anticipations  those  tones  which, 
although  belonging  only  to  the  second  chord,  are  not  tied 
over  from  or  repeated  in  the  same  part,  but  are  simply  present 
in  the  first  chord  as  harmonic  with  the  second. 

t 


225 


i=J: 


.(b) 


f 


iea^ 


w 


-rri- 


J 


£ 


P 


-f^^- 


At  h  the  bass  may  either  be  considered  as  an  anticipa- 
tion, or  the  three  highest  parts  as  a  suspension.  For  a  course 
in  composition,  or  for  the  composer  as  such,  it  is  indifferent 
which  explanation  may  be  preferred. 

Anticipations  may  occur  in  two  or  more  parts  at  once. 
226.  t  I  t 


^=J^ 


^ 


■jst. 


m^^ 


^ 


J        I 


f-r 


jfipz:;^ 


I       I 


is: 


=9^ 


^^ 


Exercise  29. 

Work  out  in  four  parts  the  following  melodies  con- 
taining anticipations. 

Model  29. 

n 


I 


m^^^^^^ 


pPrr^"^^ 


^&s^ 


G- 


i=?=^ 


9* 


i 


—     132     — 


JJi^J=^ 


iitttS 


^y^-^-^-^ 


fT-rrrr-7 


-^- 


9^ki^ 


^2 


171. 


Examples  for  Practice. 


^^^^^^^^. 


'^- a- 


:t=t: 


i 


feg^Ej; 


-iS'- 


■J— i— J- 


^— •— ^ 


!^^^^^i 


-<5>- 


172. 


aJteg^^g^^^^^Tg^^si 


fi^ 


mr|:;n^-H^H 


3^ 


-!T- 


^ 


173.  ^ 


I 


^^^a 


^^r^^^jj] 


§43. 

PEOPER  CHANGING-NOTES. 

A  tone  interpolated  between  two  harmonies  without  being 
a  chord-note  of  either,  and  progressing  at  the  same  time  by 
a  skip,  is  called  a  changing-note;  because,  although  a  foreign 
tone,  it  is  treated  like  a  chord-note,  and  thus  changes  its  har- 
monic character.     The  progi*ession  usually  leads  to  a  chord- 


—     133     — 

tone  (a,  h),  sometimes  to  a  suspension  (c).     At  d,  ehanging- 
notes  are  found  in  two  parts,  alto  and  tenor. 


227.    (a) 

i 


t         (b)  T  (c)    t         (d) 


r 


J±r^ 


;i^ii 


E=^ 


-^ 


■j^lZZZ. 


-^(U- 


§44. 

FKEE  TREATMENT  OF  FOREIGN  TONES,  AND  COMBI- 
NATIONS OF  THE  SAME. 

I.    In  the  resolution  of  suspensions,  either  the  position  of 
the  chord  (a^  b),  or  the  chord  itself  (c    d)  may  be  changed. 

(b) 


228.  (a) 


i^s^^^ 


(0) 


J(d)l 


I 


r 


TY 


r-t 


+-t 


22rca 


pi^S 


^J=^i^ii^^ 


i^i 


-^zg-arc^^^iJ 


I — ^i— r 


9i 


i 


^ 


.p-y 


:^^=i: 


-•— ^ 


-f9- 


<^ 


i^ 


-JS- ^ 


m 


f 


-^ 


—     134     — 


II.    Sometimes  the  suspension  is  resolved  by  a  skip;  aa 

a  rule  downward. 

229.    ,       ,  .       ,  U-^  I 


I  I 


i 


I^ 


li 


I        I 


J 


^^^^ppSS^H 


^t 


:^ 


t 

III.  Suspensions  in  two  or  more  parts  may  be  resolved 
one  after  the  other,  so  that  while  one  is  sustained  tlie  other  pro- 
gresses. In  such  cases  the  manner  of  resolution  may  differ  in  the 
different  suspensions. 


230. 


^ 


rr-m 


s 


i 


>» »    f> 


i 


n 


^t 


— #i- 


^i^^^ 


t:f=f-- 


J.    ± 


^Pl 


231.  (a) 


IV.    Combination  of  suspension  and  passing-note. 

S. 


r.    P. 


tufzztg: 


f  '  f 


f^» 


t=t 


^^ 


At  a  the  bass  progresses,  before  the  regular  resolution  of 
the   double   suspension   in   the   higher   parts,   to    the    passing- 


—     135 


note  e  ;  at  2*  both  lower  parts  take  the  double  passing-notes  e — g. 
The  pupil  can  easily  elucidate  the  other  examples  for  himself. 

V.    Double  suspension.    Sometimes  one  suspension  is  pre- 
ceded by  another: 


T 


The  above  is  evidently  based  on  a  simple  suspension  with 
changing  chords  (compare  I,  this  §): 


233. 


I 


r   r  r 


m^^\ 


The  next  case  is  based  on  a  suspension  quite  regularly 
ti'eated: 


234. 


— i^zJ: 


■L^J-^ 


The  combination  of  a  double  suspension  with  the  regular 
resolution  might  be  exhibited  thus: 

tT 

( 


235. 


•? 


P 


from  which,  finally,  the  first  example  given  might  be  derived. 


136 


VI.  Suspensions  also  enter  successively  from  below  and 
above,  resolution  not  occurring  until  the  last  suspension  pro- 
gresses to  a  chord-tone.  This  example  of  triple  suspension  in 
two  parts  is  from  Meyerbeer's  "L'Africaine": 


236. 


^ 


'^^ 


where  the  figuration  of  the  bass  exhibits  the  harmony  of  the 
6^-major  triad.    (Elem.  Harm.,  §  136.) 
Simple  and  common  cases  are: 


237. 


^ 


4—1- 


-G~ 


I     I 


^t 


i^ 


--^ 


—m- 

— 6*— - 

-r— 


-#— #^ 


Ife 


'^ 


Vn.    Passing-note  before  suspension  entering  freely. 


238.    ,      ,      I      I 


r 


derivable 
from: 


'^-^ 


TZ: 


E^^ 


i 


1^^ 


Older 
(former)  , 
notation: 


& ^K?- 


-^ 


Vni.    Passing-note  between  suspension  and  resolution. 


239. 


mm 


9i=t 


b^ 


—     137 


IX.    Coincidence   of  anticipation   and   passing-note   with 
progression  within  the  chord. 
Bach. 


240. 


i 


^^ 


f 


i^=g 


EE^ 


(a)  Here  the  bass  passes  through  the  intervals  of  the 
^p-major  triad,  while  the  higher  parts  progress  diatonically, 
thus  producing  the  above-mentioned  combination. 

X.  Through  the  coincidence  of  foreign  tones  with  accom- 
panying chord-progressions,  pseudo-chords  arise,  easily  deri- 
vable, by  the  aid  of  slight  rhythmic  alterations,  from  simple 
progressions  with  foreign  tones.  Each  example  below  is  fol- 
lowed by  the  simple  hannonio  form  from  which  it  was  derived. 
241.    Bach. 


m^^^F^^ 


lis 


Mendelssohn, 
t 


i 


-LA 


^m 


I         11        I         I.I  I      I     I     I        III 


aji##^^ 


I       I     I     I        II 


mi 


:t=P=i= 


A 


^#i^N^^^p 


J  J  J  ^-  J  J  J 


9-^ 


q=g 


^ 


^^m^^^^ 


—    138    — 


'^^^^^^^ 


r=n 


^^ipsi 


m 


JSL 


3^ 


i#####^#^ 


♦      S- 


X       I 


J- 


P&^^F^^E^I 


By  comparison,  the  pupil  can  easily  explain  for  himself 
similar  combinations  in  works  by  the  masters,  and  will  be 
enabled  to  attempt  such  in  the  proper  place. 

The  examples  for  practice  in  the  next  Exercise  afford 
opportunity  for  their  employment. 

Exercise  30. 

Work  out  In  four  parts  the  following  examples  for 
practice,  employing  combinations  of  foreign  tones,  but  only 
those  of  which  the  pupil  can  give  a  clear  and  satisfactory 
explanation. 


Model  30. 


I 


s^ 


U-i-. 


UM 


t 


m 

m 


i 


—     139     — 


j=^ 


J 


^  J 


££ff=^=afT=f 


^^ 


i 


1 1 


f 


W 


:k^=^i=^ 


J.^TTI  ,  J 


*t^ 


frP^ 


f=p 


4—4  r      _      i:?^^:^ 


9Sife 


^J_J_J_J 


q^^=F-r=P 


f 


174. 


#— r-» 


Examples  for  Practice. 


»=r=pc 


5e£^I 


i=t: 


^^ 


:«zizr=c:pzze 
-«W- — 


U 


^^^^BP 


p.       Snsp. 


Sus.  Sus. 


^^P^g^S 


a  175. 


140     — 


^^^^ 


^^^^ 


-»=P 


^ 


5^ 


176.    a-minor. 


a±^Et 


5 


t-=t^ 


p_=^ 


-^-Si-=^ 


^t^^a-^r^^^^^^^^Ffes 


1   •  I    I 


177. 


i 


'^;-J4-Ji.4ia. 


2i* 


?S 


1^-T^ il^ 


^^=i;: 


•  d    4 — li- 


i 


3tt*|ip^^_^ 


f^ 


int 


r«— «-#-J— • 


tifllt 


5^ 


:±3t 


-3- 


173. 


^I^^F^^^^^BSrffgTi^ 


Here  the  Chorales  mentioned  at  the  end  of  Part  I  may  be 
worked  out  with  foreign  tones;  or  folk-songs  containing  foreign 
tones  without  modulating.  An  exhaustive  treatment  of  foreign 
tones  belongs,  in  a  course  of  composition,  to  the  department 
of  Counterpoint 


'O'^O 


—    Ul    ^ 


III.  Harmonic  Modulation. 


§45. 
THE  MEANING  OF  MODULATION. 

To  modulate,  means,  to  pass  over  to  another  key.  We 
say  of  a  piece,  that  it  modulates,  when  different  keys  occur 
in  it.  Modulations  are  transient^  when  the  movement  again 
returns  to  the  original  tonality  (key);  permanent^  when  this  is 
not  the  case. 

In  the  science  of  modulation,  each  chord  is  regarded  as 
representing  a  key;  and  this  in  the  capacity  of  one  of  the 
Principal  Chords  treated  of  in  Part  I,  first  section  ;  or,  as  a 
Subordinate  Chord  representing  the  dominant. 

Only  by  the  progression  of  its  tones  can  we  recognize, 
that  a  melody  modulates  and,  consequently,  requires,  in  four- 
part  harmony  as  in  any  other,  chords  of  different  keys ;  for, 
in  many  cases,  the  occurrence  of  chromatic  signs  only  indi- 
cates, as  the  pupil  knows  from  the  exercises  in  Part  II,  the 
presence  of  foreign  tones,  which  in  themselves  do  not  change 
the  key. 
242. 


3 


S 


-<5»- 


* 


E 


'=^ 


-G- 


■^*- 


m 


s 


p 


3 


s^^ 


«$•- 


m 


In  the  above  (7-major  melody  the  first  /*j(  will,  it  is  true, 
be  regarded  merely  as  a  chromatic  passing-note,  for  we  cer- 
tainly have  no  occasion  to  suppose  that  the  key  is  conti-adicted 
in  the  first  measure.  But  the  second  /"jj,  if  harmonized  as  a 
suspension  in  (7-major,  would  paralyze  the  entire  movement. 


—     142     — 


243. 


BE 


Ji 


J  bad 


« 


rr«f 


-&- 


^ 


J.^^JJ   Ji  J   i.J^i  J    J  i 


^ 


^ 


-P— #^ 


'f 


4= 


ri- 

We  must,  therefore,  think  of  some  new  key.     But  which? 

The  progression  g-h-d-h  in  the  melody  indicates  (r-major 
clearly  enough!  —  G-major  is,  therefore,  to  be  introduced. 

But  in  which  chord  of  the  new  key  is  /*J|  contained? 

It  is  found  in  each  of  the  principal  dissonant  chords.  As 
/"ji  lies  in  the  soprano,  the  chords  of  the  ninth  and  minor 
seventh  are  excluded,  thus  leaving  the  chord  of  the  dominant 
seventh  and  the  diminished  triad.  As  the  dominant  chord 
fixes  the  new  key  more  decisively  than  the  diminished  triad 
(§  21),  we  choose  the  former,  thus  : 


244. 


^^^ 


-U- 


k  I 


i^'j  i  i  i 


1; 


f 


^i 


--*«- 


:i: 


The  further  progression  corresponding  at  first  with  the 
opening,  we  choose  for  the  present  the  first  harmony. 

§  46. 
CHANGE  OF  MODE. 

The  transition  from  one  key  to  another  of  like  name,  as 
from  C-major  to  C-minor  and  reversely,  is  not  properlii  a 
modulation;  because  the  relation  to  a  particular  tone  as  fun- 
damental or  Jcey-note  (Elem.  of  Harm.,  §  50)  is  not  ubaudoued, 
(for  the  same  tone  retains  this  capacity),  but  merely  the  mode 
is  changed. 

Thus,  directly  after  any  tonic  triad,  that  of  the  like-named 
key  may  follow,  and  the  new  mode  may  be  adhered  to  there- 
after as  long  as  desired. 


—     143     — 


aa. 


Thus  in  minor  movements   the  major   triad   occurs   very 
frequently  as  the  closing  chord. 

1: 


247. 


m 


i-a 


And  in  major  movements,  the  principal  dissonant  chords 
of  the  minor  Tcey  appear  with  major  resolutions: 


I 


*^EE^ 


t=toc±z:=B 


likewise  the  sub-dominant  triad  of  the  minor  heij^  and  also  its 
substitutes^  with  progressions  to  major: 


249. 


i 


f=x-r 


9^ 


f 


rr 
m 


1= 


I 


—      144     — 

while  on  the  other  hand,  those  principal  chords  of  the  major 
Jcey  which  do  not  contain  the  major  sixth  of  the  latter,  such 
as  the  dominant  chord  and  the  diminished  triad,  may  be  at 
any  time  resolved  to  minor. 


i^i^^srt^^ 


250. 


g^ 


J  i  i  ^    i 


T^'^ZZV^ 


feSEfi 


-^^ 


On  the  contrary,  those  chords  of  the  major  key  possessing 
the  major  sixth,  the  major  chord  of  the  ninth  and  minor  chord 
of  the  seventh,  resist  this  resolution. 


251. 

Never, 
therefore: 


^^i 


-^^f: 


I 


-7!^- 


^^- 


^ 


§47. 

MODULATION   TO   ADJACENT   KEYS. 

Nearly-related  and  relative  keys  follow  each  other  directly; 
as,  in  the  next  examples,  one  tonic  tiiad  follows  the  other, 
the  triads  of  the  new  key  sufficing  to  introduce  the  same: 


252  C-major.  |    j  G-major  |         j     C-major.     j      j  F-major.  | 


^^ 


lc=X 


—     145 


C-inajor.    I    I  a-minor.  I  I    c-iniuor.    I      I  g-minor.  I 


i^ 


g^a: 


3i: 


--W=W=t- 


:t=t 


m: 


t^ 


f-minor. 


minor.      I       I 


c-minor. 


1|-^ 


i     I 


:ji=oi. 


major. 


I     I     I 


■r'p  s 


^^^=^^^ 


tR: 


:1JF 


:t 


I     M    I 


?^£ 


i 


^g^ 


Or  the  tonic  triad  of  a  key  is  followed  by  a  dissonant 
principal    chord   of  the   related   or  relative  key,   which  then 
resolves  regularly  to  the  tonic  triad  of  the  latter: 
253.    C  G  C  F  S  .     a 


I     I    I    r      I     I    I    I  '    ' 


I 


gi^ 


i^^jg: 


m 


fc^S 


E> 


feaa^;;^3a>feidE5bfeiN^E^^Jl 


^frr"ff^""=^='=' 


?g^zn-^i^ii^R5g^-3ag±J=Fi 


Here,   too,    the    dominant   triad   may   be   substituted,    in 
suitable  cases,  for  the  chord  of  the  dominant  seventh. 

i 


254 


i^ 


Bussler,  Elementary  Harmony. 


10 


—     146     — 

The  subordinate  triads,    and   subordinate    chords   of  the 
seventh  on  the  second  degree,  may  also  be  readily  employed 
in  connecting  keys  so  nearly  related. 
255.    C  G C   a c g 


'  '  I  I   I    '  I  I   '   I      I  T'  '   I  '  I 


^^1 


^te 


c El? C      G 


9^ 


^^ 


^^^m 


-li — 1 


^      I    I    r  r     -F 


Eb. 


I       I       I      J  I 


E^^^ 


1  I  I 


w 


p=|i=:za: 

r-^i — r 


The  following  melody  contains  modulations  of  this  kind. 

256.  C G C_ 


N^^ffW^^W 


„U=, 


yyi 


:&=^^-p=P=tT— r— ^=3ig 


i^B^: 


ir=fii 


F 


3: 


147 


In  all  these  cases,  it  is  the  close  relationship  between  the 
keys  which  connects  them.  Though  common  tones  are  usually 
prominent  in  this  connection,  which  tones  will  hereafter  be  the 
essential  connecting-links  of  the  modulation,  this  must  here  be 
regarded  as  accidental,  although  a  natural  result  of  the  rela- 
tionship. The  distance  between  keys  in  the  circle  of  fourths 
and  fifths  determines  the  degree  of  relationship.  (Elements 
of  Harmony,  §  53). 

A.  The  Dissonant  Principal  Chords 

as  a  means  of  modulation  from  the  tonic  triad  of  a  key  to  that  of 

any  other  key, 

§  48. 
GENERAL  SKETCH  OF  THE  PROCEDURE. 

The  usual  procedure  in  a  modulation  consists  in  the 
introduction  of  a  dissonant  principal  chord  of  the  new  key, 
and  its  resolution  to  the  tonic  triad  of  the  latter. 

RULE:  The  introduction  of  the  dissonant  principal  triad 
must  be  prepared  by,  at  least,  one  common  tone  present  in  the 
preceding  chord. 

C-maj.  to  B-maj.        C-maj.  to  DJ?-maj. 


257. 


^i 


■-^^ 


if^^^ 


I 


An  exception  to  the  above  is  found  in  the  few  cases  dis- 
cussed in  the  last  §,  in  which  the  dissonant  principal  chord 
of  the  related  or  relative  key  has  no  tone  in  common  with 
the  preceding  triad.  In  these  cases,  the  close  affinity  of  the 
keys  renders  such  a  mediation  superfluous.  Still,  even  these 
modulations  may,  of  course,  be  effected  according  to  the  given 
rule  The  pupil  should  in  each  case  carry  them  out  in  both 
ways;  e.  g.:a-minor  to  (7-major: 

10* 


148     — 


258. 


^i=± 


f^ 


-\=-^ 


Where  the  dissonant  principal  chord  has  no  tones  in 
common  with  the  preceding  triad,  a  chord  is  introduced  be- 
tween them  having-  tones  in  common  with  both,  and  capable 
of  following  the  first  chord  within  the  limits  of  one  key, 
according  to  the  regulations  given  in  Part  I. 

This  interpolated  chord  can  either  be  a  triad,  a  chord  of 
the  sixth  (as  below  at  a,  c),  or,  if  it  admits  of  treatment 
according  to  the  given  rules,  a  chord  of  the  fourth-and-sixth  (h). 

To  facilitate  the  leading  of  the  parts,  the  given  tonic  triad 
may  also  be  taken  as  a  chord  of  the  sixth  (d).  In  the  course 
of  harmonic  progressions,  modulations  likewise  occasionally 
follow  a  chord  of  the  4  (e)^  without  affecting  the  regular 
treatment  of  this  latter. 


(b)  C-e. 


m 


^^ 


m^ 


F^ 


:ti=t^ 


I 
§  49.. 

CROSS-EELATION. 
As  modulation  brings  chords  of  distant  keys  into  imme- 
diate  contact,   it    also   unavoidably   induces   very   harsh   bar- 


—     149     — 


monic  progressions.  By  a  skilful  leading  of  the  parts,  these 
may,  however,  be  quite  avoided  in  most  cases,  and  much 
softened  in  others.  The  so-called  cross -relation  often  occurs 
in  modulating. 

I 


260. 


^^=P 


:8^itte 


-oi 


^r 


Cross- relation  results,  when  any  tone  in  one  part  is 
followed  by  [or  enters  together  with]  a  tone  in  another  part 
which,  though  bearing  the  some  root-name  (letter-name)  as  the 
first,  is  higher  or  lower  by  a  semitone,  and  enters  by  a  skip. 
It  makes  no  difference  whether  the  tones  forming  the  cross- 
relation  lie  in  the  same  octave,  or  in  different  octaves.  In  the 
following  examples 


261. 


(a)  ,       (b)  (c)    .  (d) 

W— iTr#--'-Tr-/--Tr'-^-^^ni 


the  cross -relation  is  found  at  (a)  between  soprano  and  alto, 
at  (h)  between  soprano  and  tenor,  at  (c)  between  soprano 
and  bass,  at  (d)  between  alto  and  tenor. 

The  factors  cooperating  to  form  the  cross-relation  are: 

1.  Two  tones  belonging  to  the  same  root -degree  and 
differing  in  pitch  by  a  semitone  enter  in  immediate  succession 
(i.  e.:  two  tones  which  form  a  chromatic  semitone  [augmented 
prime,  augmented  or  diminished  octave]), 

2.  In  two  different  parts, 

3.  The  second  tone  entering  by  a  skip. 

The  cross-relation  is,  therefore,  never  present,  when  the  two 
different  tones  of  the  same  root-degree  lie  in  the  same  part,  this 
latter  progressing  by  a  degree  (chromatically)  ;  as  : 


—     150     — 


262. 


^^il^^S 


-^ 


^- 


-i?^. 


-^-^- 


i 


and  it  may  in  this  manner  be  avoided  in  modulation. 

But  when  other  reasons  exclude  this  procedure,  e.  g.rwhere 
a  given  melody  leads  to  the  cross -relation,  it  should  at  least 
be  avoided  in  the  outer  parts. 

Good  vocal  leadings  justify  any  cross-relation. 

I      .         .      I      ) 


263. 


§  50. 
CHORD  OF  THE  DOMINANT  SEVENTH  IN  MODULATION 

Exercise  31. 

Modulate  with  the  dominant  chord  of  the  seventh  (I)  as 
a  written  exercise,  (2)  without  notes  at  the  instrument: 
from  C-major  to  every  major  key, 
from  C-major  to  every  minor  key, 
from  C-minor  to  every  major  key, 
from  C-minor  to  every  minor  key. 
Carry  out  like  modulations  from  a  key  having  a  signature 
of  many  sharps  OP  flats  to  any  other,  keys,  even  to  those  v^hose 
signatures  do    not   occur,   but    with    which    we   are   acquainted 
through  the  Elem.  of  Harm,  and  Not.,  §  47  ;  such  as  6rii-majop, 
cib-minor,  etc. 

Chief  rules,  and  examples,  are  given  in  §  48. 
A  few  special  directions  may  follow  here: 
1.    In  this  exercise,  and  similiar  ones  to  follow,  the  pupil 
should  aim,  by  the  positions  of  the  chords,  to  render  every 
transition  as  agreeable  to  the  ear  as  possible.     Nevertheless, 


—     151     ~ 


some  will  result,  which  despite  all  regularity  sound  hard. 
But  in  the  proper  place,  as  parts  of  further  combinations  which 
are  totally  lacking  here,  such  transitions  may  not  only  be 
justifiable,  but  really  effective.  At  all  events,  familiarity  with 
them  belongs  to  the  composer's  mental  equipment. 

2.  In  modulations  starting  with  the  minor  triad,  the  pupil 
should  avoid  making  the  minor  tliird  of  the  minor  tonic  triad 
the  leading-note  (third  of  dominant  chord)  for  the  key  to  be 
introduced.     Therefore, 


264. 


not:  ) 


a-minor  to  D[?-major. 


but: 


f9' 


■^i=£.-=^ 


^^^^ 


^ 

'-^- 


P= 


The  introduction  of  the  augmented  chord  of  the  sixth 
would  justify  even  these  modulations  as  enharmonic  modula- 
tions. Their  isolated  occurrence  in  master -works  does  not 
impeach  the  validity  of  the  above  rule. 

3.  For  the  modulation  from  (7-major  to  Cft-major  or  (7b-major 
no  triad  offers,  which  by  itself  would  serve  as  a  connecting 
link.     Two  chords  must  consequently  be  interpolated  here, 
265.    C  C[?  C  ^Cjf 


t4~- 


-^^^B^^^m 


■iz^\ 


:r^ 


2^ 


:t=z: 


:b^ 


^i 


By  the  aid  of  enharmonic  changes  (Cj-major=Z)[?-major, 
^[7-major  =  5-major)  both  modulations  may  be  carried  out 
without  interpolating  a  chord. 


266. 


—     152     — 

Such  cases  are  also  met  with  in  the  other  exercises  in 
modulation.  The  pupil  should  always  carry  them  out  in 
both  ways. 

4.  The  dominant  triad  may  be  substituted  for  the  domi- 
nant chord,  when  the  thus  omitted  seventh  is  present  in  the 
preceding  chord. 


267.  < 


"m 


M 


* 


^rtii^ 


1^^ 


I 

Remark.  A  modulation  is  diatonic  which  employs  only 
diatonic  intervals;  chromatic,  when  it  employs  the  chromatic 
semitone;  enharmonic,  when  an  enharmonic  change  takes  place. 

Exercise  32. 

Harmonize  the  following  melodies,  overladen  with  mod- 
ulations, modulating  by  aid  of  the  dominant  chord. 

Model  31. 


IT  rr  TTT? 


»^^^f=^fl=»-P4f^f 


TTf  f  sfTf  ^T f  f 


ffiEgEa 


^ 


178. 


BEE 


i=tt 


fcES 


—     153     — 

Examples  for  Practice. 


i 


t:=t=:ttzz5f:: 


l^ 


l^^^^^^^^^^ 


l^^t^s^^^^gg^^ 


181. 


^Sl 


itzte: 


»?=E 


tiit=t 


182. 


?^f3 


iieErJ^ 


183. 


cff-^q: 


^E?^EfeiEtE^Et3 


i 


g^J^'L.r^_4,jgg^jr^g^j^j^_gi=^|gzgp 


184.  


i 


:ir=^ 


:t=5=5 


FTt^y 


t=:t=±t=^JE^^^E?^=E^E^ 


t=[:: 


268. 


§  51. 
HARMONIC  SEQUENCES. 


m^ 


^F^^^=^^^^ 


F 


^ — ,. 


:^^^ 


—     154     — 


;?i 


rrf 


^^n 


,1 


I     I 


JeeS 


I 


:^p: 


¥-T~^- 


r^r 


i 


On  examining  this  last  example,  we  perceive  that  the 
same  modulation  is  repeated  several  times  on  different  degrees, 
all  parts  progressing  continuously  and  regularly.  Such  har- 
monic successions  are  called  harmonic  sequences. 

In  our  example,  the  modulation  always  passes  from  one 
key  to  another  in  the  fifth  degree  of  affinity,  1.  e.:  whose 
key-note  is  a  semitone  higher;  and  occasionally  employs  the 
enharmonic  change. 

The  regularly  repeated  modulation  of  a  sequence  is  called 
its  motive.  The  motive  of  the  present  sequence,  which  is  the 
modulation  by  the  dominant  chord  into  that  key  whose  key- 
note lies  a  semitone  higher,  is  marked  out  under  a.  It  fills 
exactly  one  ^/^  measure.  Each  succeeding  measure  is  a  repe- 
tition of  tlie  same  a  semitone  higher.  In  common  time  this 
motive  might  take  on  the  following,  or  many  other,  rhythmical 
forms. 


269. 


3: 


-^-^v 


m 


t 


-^^Jr-\,J- 


t=:it 


-b* 


g^^^ten^ 


The  same  sequence  may  he  exhibited  in  more  condensed 
form,  by  contracting  the  last  and  first  chords  of  each  two 
suecessive  repetitions  of  the  motive  to  a  single  chord. 


—     155     — 


^^^^^^^ 


A  few  motives  for  sequences  follow,  with  indicated  pro- 
gression, whose  working-out  is  left  to  the  pupil. 


Motive 


271. 


etc.      (b)  Motive 


etc. 


_^>=|zfa^g=|g^r^^^^ 


Motive  etc.         Motive 

ry — #— ^^^ — • — ^"T—r"       II 


etc. 


i 


:^»^^p4"i-^ 


Motive 


etc. 


Motive 


etc. 


^^^^^m 


jj  ji  i"^ '/ ' 


f^=^ 


^^B^^^#g^^^S] 


The  manner,  or  style  in  which  a  sequence  is  to  be  carried 
out,  i.  e.:  how  the  regular  connection  of  the  repetitions  is  pro- 
duced, is  not  always  achieved  according  to  the  principle  of 


'\/^yv 


—     156     — 


absolute  symmetry  hitherto  observed.  Thus,  sequences  may  be 
formed  by  alternating*  in  mofZe,  which  admit  of  greater  unity 
in  the  modulation  by  not  receding  so  far  from  the  first  key. 


272.    ,— ^ 


m. 


I  I 


f- 


^^ 


The  strictness  in  progression  may  also  be  modified  in  favor 
of  a  diatonic  leading.  Thus,  in  the  following  sequence,  the 
modulation  always  leads  into  keys  based  on  intervals  of  the 
diatonic  scale. 


273.    C 


et 


G 


bt 


I  |^j=pit±=i#|3^^T^ 


^UM=^,l^U,i4d,^ 


i 


^ 


f 


The  close  would  perhaps  be  better  so: 
at  b  C 


274.     I 


this  modulation  not  leading  so  far  away  from  the  chief  key. 
In  this  sequence,  not  only  the  mode  changes,  but  changes 
also  occur  in  the  leading  of  the  soprano  in  the  two  places 
marked  f.  However,  it  is  on  the  whole  decidedly  preferable 
to  the  following  in  absolutely  strict  progression: 


—     157     — 


275^ . 


wherein  all  connection  with  a  fixed  key  is  quite  lost. 

N.B.  To  enable  a  further  extension  of  the  sequences,  it 
is  here  permitted  to  overstep  the  compass  of  the  voices. 

Exercise  33. 

Form  sequences,  using  the  dominant  chord  in  modu- 
lating, (I)  in  writing,  (2)  without  notes  at  the  instrument. 

Here  the  inversions  should  not  be  neglected.  No.  275  shows 
the  ascending,  No.  271  &  the  descending  chromatic  scale.  Set 
the  chromatic  scale  also  in  the  bass  and  inner  parts.  Proceed 
in  like  manner  with  the  enharmonic  scale  in  Nos.  270  and  271  a. 

§  52. 

MODULATORY  PHRASES. 

In  composition  and  musical  practice,  it  is  often  desirable 
to  carry  out  a  modulation  through  a  long  succession  of  chords, 
with  avoidance  of  all  harsh  progressions  and  abrupt  transitions; 
i.  e.:to  form  a  modulatory  phrase.  With  nearly-related  keys, 
connective  subordinate  triads  are  interpolated,  and  a  cadence 
added. 


276. 


with   distantly -related   keys,  a   connection   is   sought   by    the 
gradual  introduction  of  distinctive  tones. 


—     158     — 


277. 


Exercise  34. 
Form  modulatory  phrases  from  Major  to  Major. 

from  Minor  to  Minor, 
from  Major  to  Minor, 
from  Minor  to  Major. 

§  53. 
MAJOR  CHORD  OF  THE  NINTH  IN  MODULATION. 
The  major  chord  of  the  ninth  admits  (§  46)  of  a  regular 
major  resolution.    It  is,  therefore,  employed  only  in  modulating 
from  a  major  or  minor  key  to  a  major  key. 

A-maj.    —    G-maj.     a-min.    —    G-maj. 


278. 


H 


&- 


\ 


^i 


-G- 


G- 


^^^ 


Employment  of  it  restricted  by  the  difficulty  of  introducing 
the  major  chord  of  the  ninth.     (P.  39,  40.) 

Exercise  35. 

Modulate  (I)  in  writing,  (2)  at  the  instrument,  with  the 
major  chord  of  the  ninth  from  major  and  minor  l<eys  to 
major  keys. 

Form  harmonic  sequences  with  same  chord.    E.  g. : 

-J  J  J     

\  ^     \     r    "r    ^    "^f^    -G-      i     r    ■     i     ^r    ^ 

279. 


—     159     — 


§  54. 

MINOR  CHORD  OF  THE  SEVENTH  IN  MODULATION. 

The  minor  chord  of  the  seventh  in  major  also  admits  of 
no  resolution  to  minor. 

Exercise  36. 

Modulate  with  the  minor  chord  of  the  seventh  (I)  in 
writing,  (2)  at  the  instrument,  from  Major  to  Major;  and 
from  Minor  to  Major.    E.  g.: 

C-maj.  —  B[7-maj.  a-min.  —  B[;-inaj.  C-major     —     A-major. 


280. 


p^:^^^g!=I^ElkgJ=g: 


-G-      •^- 


gi^BS 


.Q. GL- 


^; 


JCk <2_ 


Form  harmonic  sequences  with  same  chord.    E.  %, 


281. 


I 


& — «> 


&- 


% 


>& 2? 


.^6i- 


-9^- 


n 


^^ 


1 


11 


Harmonize  the  following  melodies  with  the  major  chord  of 
the  ninth  and  minor  chord  of  the  seventh  ;  and  form  modulatory 
phrases  with  both  chords. 


Model  32. 


—     160     — 


ifff^^ 


I  r 


-5*^ 


-<»- 


^&^^,U=.l 


Examples  for  Practice. 


^^=^ 


t=t 


^^ 


=1: 


:#=t: 


:t=i 


^*=?=?=bF 


a^=B 


-<9^ 


:^ 


fiz^izi^ 


:ti:: 


M 


tT=P 


P^t 


^  u  187. 


3^^^^ 


S 


-(S^ 


:t=t=J: 


:p=1^ 


*t 


5^3^S^ 


§  55. 
MINOR  CHORD  OF  THE  NINTH  IN  MODULATION. 
The  minor  chord  of  the  ninth  belongs  to  the  minor  key, 
but  may  also  (§  46)  be  resolved  to  major. 


Exercise  37. 

Modulate  with  the  minor  chord  of  the  ninth 
from  IVIinor  to  Minor, 
from  Major  to  Minor, 
from  Major  to  Major, 
from  Minor  to  Major. 


—     161     — 


282. 


E[?  -  0. 


liE&d^l^g^ 


-b<2 r-b^- 


i 


I    L     I 


I 


-(^ 


9i 


-^ 


-' "-] — 

E^ ^=^ 


Employment    of  it  restricted  by  difficulty  of  introduction. 

§  56. 
DIMINISHED  CHORD  OF  THE  SEVENTH 
The  diminished  chord  of  the  seventh  resolves  (§  46)  to 
minor  or  major.     After  the  dominant   chord,   it  is  the    most 
serviceable  chord  in  modulating. 

Its  multifarious  signification  as  an  enharmonic  chord  will 
be  noticed  later.  For  the  present,  the  pupil  should  resolve 
each  diminished  chord  of  the  seventh  in  accordance  with  its 
notation. 

Exercise  38. 
Modulate  with  the  diminished  chord  of  the  seventh 
from  one  minor  l<ey  to  every  other  minor  key, 
from  one  major  l<ey  to  every  minor  key, 
from  one  minor  key  to  every  major  key, 
from  one  major  key  to  every  other  major  key.  E.  g.: 

C  —  D.  C  —  d.  c  -  D.  c  —  d. 

SI 


* 


Eg%il^lfci3 


»S=±t^g^g: 


'^ 


g^^lSjIg^i^B 


jy 


-iS2- 


S^fii 


Form  sequences  with  the  dimin.  chord  of  the  seventh. 

Bussler,  Elementary  Harmony.  11 


162 


s^i^^tei^ 


^r-> 


^ 


ry 


:t=4 


In  freer  sequences,  like  No.  272,  one  may  alternate  be- 
tween the  minor  and  diminished  chords  of  the  seventh. 

Form  modulatory  phrases  with  the  diminished  chord  of 
the  seventh.  Form  the  chromatic  and  enharmonic  scales 
(Exercise  33)  with  the  diminished  chord  of  the  seventh. 

Exercise  39. 

Harmonize  the  following  melodies.  These  principally 
give  occasion  for  employing  the  diminished  chord  of  the 
seventh;  also  occasionally  the  minor  chord  of  the  ninth  and 
other  chords  heretofore  used  in  modulating.  Some  begin  with 
dissonant  chords  (like  the  Model),  No.  201  even  in  a  key  at 
variance  with  the  signature,  i.  e.:  with  the  seventh  of  ^-minor, 
the  exercise  being  in  jBj? -major.  The  conditions  explained  in 
§  46,  more  especially  the  resolution  of  chords  in  the  minor 
mode  to  major,  and  the  alternation  of  dissonant  principal 
chords  (§  22),  are  applicable  here. 

Model  33. 


g^*«^te 


LT  t  crrt 


—     163 


Im^i^^S^ 


|t=iiJ=tt.^=j^-4^-pH-j-^ppn 


5« 


j^^aM/T^i^ 


Examples  for  Practice. 


188.  ,  ^ 


189. 


ii 


pBii 


m 


-^9— /5^ 


fe^ 


t=t 


G——^ 


-^^ 


t=t 


^^ 


Ei 


190. 


itep^^^^^^^^^^^^g^ 


191. 


gM^OHZIE^Pfapigg^ 


f|^ 


^^EB 


§iS 


^ 


^= 


nr 


t=t 


11 


—     164     — 


192. 


^^^^^^^^^^^^^^^ 


193 


■f^^- 


^^^^^ 


^^^r=nt=r 


J L— I 


iiisi 


^^^^^^^^^m 


194. 


• ,— (5i 


iSi^"EB^g:i^S3E^E^ 


^^^^^^^^^^^^^^ 


t^^#^^^^^^^^ 


^^^P^a^^Eg 


=?=^^ 


^8^ 


^T^^f=Fr 


196.    Andante. 


;eE^^^^§LS^^^^^ 


:Ee^: 


I^^^^^^M^^ 


^55d^^Ep^^>E^lEiSi 


197. 


225ESEEg: 


BS3 


5EEfa^;^J^-^^feE^ 


198. 


gg^-^p^g^^ffi^A^^ 


—     165     — 


'k^^H^ 


i=[ 


::-[:: 


w=ir 


x=^ 


i^^^^^^^ 


W- 


199. 


^^i^^^^S^ip^l 


^^^^^^g^ip^ 


^^^^^Si^E^^^&S 


t^g.^^^ 


^^^^^ 


i^S^^EE 


?l^ 


S 


&-fo^^ 


t=T=t: 


^x=i: 


lO: 


t==t=t 


.«5r?_ 


^^S^^^^^^ 


=±=2tl±=t 


202. 


f^?^£tnrf33feTjteai!a33F 


e^ 


;^ 


I 


.  »  203. 

gfig-^l  I  P      • 


Ee 


±=t: 


f^rr? 


1 


-fz^^^^ 


a=^ 


E 


jST-^grrp: 


->'— ^ 


¥ 


fcS: 


204. 


'^zj^'ih^s^^ 


-     166     — 


^^^^^^ 


Fir^FF^ 


fe^i?=i 


^^1^^ 


§  57. 


e^-  g^-  b  -  d. 

cx-  ei-  g^-  b* 


ENHARMONIC  CHARACTER  OF  THE  DIMINISHED  CHORD 
OF  THE  SEVENTH. 

Every  diminished  chord  of  the   seventh  belongs,  through 
the  enharmonic  change,  to  four  different  keys,  e.  g.: 
h  -  d  -  f  -  a\f^    (7-minor;  fundamental  chord  =  h  -  d  -  f  -  a^, 
h  -  d  -  f  -  g%     a-minor;  ^  ^      =g^-h  -  d-  f, 

h  -  d  -  e^-  g%   /j}-minor;  ^  „ 

h  '  Cx-  cj-  g%  (?j -minor;  „  ^ 

In  each  of  these  significations,  it  may  also  resolve  to  the 
like-named  major  key  ;  thus,  in  the  present  case,  to  6-major, 
^-major,  i^jj-major,  ^h-major  (/)jt-major). 

There  are,  consequently,  but  three  diminished  chords  of 
the  seventh  containing  different  tones  each  from  the  other; 
those  remaining  are  mere  enharmonic  changes  of  these  three. 

Exercise  40. 

The  following  melodies  afford  opportunity  for  applying 
the  enharmonic  character  of  the  diminished  chord  of  the 
seventh. 

Model  34. 

^S  =  bi^  .       ?        I       L  I     T        I 


^ 


SI 


a¥=r¥^ 


t 


■^-§. 


! — \ 


This  last  may  also  be  written  d-f-a\?-cV,  in  ^b-minor. 


—     167     — 


i- 


m 


bt? 


-G- 


m^ 


m 


i 


U^ 


cr-f 


m- 


G^ 


G^ 


Examples  for  Practice. 


205. 


B^^^^^^^^^^f=^f^t 


^^,.^p^=^^^^^^^^^ 


206. 


t=E 


g^^S^E^=^g=g 


=^=1- 


3=t2^: 


V:=X 


'^ 


-m^^^^^^^^^ 


207. 


ISEgE^J^^^-E^ 


ip: 


i::=t 


^^S^^S 


jrryfr^" 


1 — I — r 


^S 


0—fSh 


—     168     — 


208. 


^- 


i2=t2i: 


^^^^gssiJs^^^i^i 


^^ 


§  58. 
THE  DIMINISHED  TRIAD. 

Among  the  dissonant  principal  chords,  the  diminished  triad 
is  that  least  adapted  for  decided  modulations.  Its  service- 
ableness  depends  chiefly  upon  the  tones  preceding  it,  for  only 
through  these  does  it  gain  a  tendency  toward    a  definite  key. 

Inasmuch  as  it  may  be  regarded  as  a  fraction  of  a  dimin- 
ished chord  of  the  seventh,  it  may  participate  in  the  enhar- 
monic modulations  of  this  latter: 

h  '  d  -  f,    (7-major  (minor);    fundam.  chord  =  6  -  d  -  f, 
c^-  d  -  f,  e[7-minor;  „  ^^     ==d  -  f  -(a'r^)-c\}. 

b  -  d  -  cjj,/'j}-minor;  „  „     =e^-(gp-  h  -  d. 

Exercise  41. 

Modulate  with  the  diminished  triad 
from  Major  to  Major, 
from  Major  to  Minor, 
from  Minor  to  Major, 
from  Minor  to  Minor. 

286.    C  dC  be  Dc  r 


I 


IS 


^ 


^-^^^^^^^■. 


^ 


:& 


W 


3^1 


§  59. 
SUBSTITUTES   FOR  THE  SUB-DOMINANT   AS    AGENTS 
IN  MODULATION. 
As  agents  in  modulation,  for  wliicli  we  till  now  liave  em- 
ployed interpolated  triads  or  their  inversions,  the  substitutes 


—     169     — 


for  the  sub -dominant  of  the  key  to  be  introduced  may  also 
serve,  in  their  regular  progression  in  cadence-form;  progressing, 
either  through  the  dominant  chord,  or  through  the  chord  of 
the  4  and  dominant  chord,  to  the  tonic  triad. 

C-major  to  e-minor. 

t  t 


I  •  ■  -I 

For  introducing  these  chords,  the  rules  given  in  Part  I 
must  be  carefully  observed. 

Freer  introductions  of  subordinate   chords  on  the   second 
degree  are,  (according  to  §  26),  as  follows: 
I 


288. 


m 


e^gs 


m 


C-major. 


■^' 


:^ 


-t 


ui    n 


m 


a-mmoiv 
d 


n 


a 


a-mmor  V 
C-major 


IV 
II 


Exercise  42. 

Modulate,  through  agency  of  subordinate  triad  II  in 
major,  (I)  from  Major  to  Minor,  (2)  from  Minor  to  Minor. 

Modulate,  through  agency  of  subordinate  triad  II  in 
minor,  (I)  from  Major  to  Minor,  (2)  from  Minor  to  Minor 


—     170     — 

Modulate,  through  agency  of  the  subordinate  chord  of 
the  seventh  in  minor,  (I)  from  Major  to  Minor,  (2)  from 
Minor  to  Minor. 

Form  modulatory  phrases  with  all  material  now  at 
command. 

Exercise  43. 

Harmonize  the  following  melodies,  which  give  occasion 
for  modulation  with  the  subordinate  chords. 

Model  35. 


i 


^ 


^ 


m^ 


■^ 
ji^ 


$=^ 


tTf 


r^ 


— ^sH 


f 


9^ 


msm^^E^^m^ 


^^^. 


^i^ 


-L^^k^^^MJA 


§26. 


1= 


Examples  for  Practice. 
Tones  marked  f  are  to  be  harmonized  with  one  of  these 
subordinate  chords. 


26. 


209.. t  t  t 

+  +  210. 


v=x 


m 


s 


3^ 


ES 


—     171     — 


i 


pri=i 


^^^^^S^f^i^ 


\=t 


lr=^-- 


$^^^^^^^^ 


211. 


±f 


'^m 


^-Si 


s 


:^t 


F^fe^ 


212.. 


^»— • 


^ 


^EE^ 


±-s- 


^fe^.^^ga^f^£i:^ig 


i— B^ 


ffj 


J=f=es^=l.-=i- 


gtf— t— p 


3£ 


^s§^ 


B.    Deceptive  Progressions. 

§  60. 
MEANINa  OF  "DECEPTIVE  PROGRESSION". 
The  dissonant  principal  chords  were  at  first  restricted  to 
eertain  progressions  of  the  separate  parts. 


289.   E^^^^Eipfe 


We  were  then  permitted  to  free  single  parts  from  the 
strict  resolution,  in  order  to  better  the  melody,  the  leading  of 
the  parts,  or  to  secure  a  fuller  harmony. 

.  290.  I  I        I        I        I 


r 


^' 


• — ^- 


i^s 


2 


<5»— -^ 


r  rr  f 


But  that  chord,  to  which  the  dissonant  chord  was  obliged 
to  resolve,  remained  unaltered  by  these  liberties,  1.  e.:  was 
always  the  tonic  triad. 


—     172     — 

This  rule  too  must  now  be  annulled  in  favor  of  further 
artistic  freedom.  We  shall  form  progressions  of  dissonant 
principal  chords,  which  do  not  lead  to  the  tonic  triad,  but  to 
other  chords  of  the  same  or  other  keys,  as  may  be  desired. 


291. 


i^^^n^^n 


^1 


9t 


m 


J2.      £L 


f^lf 


g> ST. 


1^ 


Such  progressions  are  called  deceptive. 

As  agents  in  forming  deceptive  progressions  we  have 

1.    Common  Tones: 


292. 


1^ 


-<9 — 


&- 


6?— 


|^6>— g^-|^-6^-fe   -'  fe^J 


-^- 


-b^- 


^   b^ 


l^e^^l^l 


2.    Near  relationship  of  the  keys: 


293. 


gy — T 


— ^s*- 


:s 


C      G 


C      F         C       e  •    A^(VI) 


^l^^gQi^gJ 


5fc 


J2.    ^       J2.    ^       n. 


11 


Z2.   8.0. 


-t-^- 


i 


3.    Partial  regularity  of  resolution: 


294. 


F      G> 


F      c 


^^sy^s^^^p 


In  all  cases  great  care  is  required  in  the  leading  of  the 
parts;   this  may  occasionally  be  benefitted  by  foreign  tones. 


173     — 


§  61. 
DECEPTIVE  PROGRESSIONS  OF  THE  DOMINANT  CHORD. 

We  suppose  the  dominant  chord  of  a  key  to  be  given, 
and  progress  from  it,  through  deceptive  progressions  according 
to  the  above  rules,  to  any  desired  key. 

The  deceptive  progression  may  lead  to  a  triad: 


295. 


Mozart. 


etc. 


7^ 


W 


To  a  dissonant  principal  chord: 


296. 


r — <& — <9- 


itzg-gzttig-^- 


izzzs: 


4^ 


-G—G- 


-G-9& 


-G—G- 


-iBr]^r?- 


Wagner. 
("Lohengrin"). 


^pl^ 


.iiL   ^ 


^f=^'i;^^s^ 


-p— <g 


^—. 


p^ 


To  the  subordinate  chord  of  the  seventh  (which  here,  as 
elsewhere,  is  often  stubborn): 


297. 


8«=? 


■G-\ 


tZ^-a,-..>4P 


lEi^E-gE^gER^f 


'G-—0- 


-G    \}Cf    #- 


4^ 


e 


3T=S=^ 


-i^ <9- 


i2.t7jJZ^  .^ 


•?g — gy~»- 


a 


We  see,  that  each  modulation  can  be  effected  in  various 
ways;  and  it  is  excellent  practice,  to  work  out  each  as  variously 
as  possible. 


—     174    — 


Exercise  44. 

Form  numerous  deceptive  progressions  of  the  dominant 
chord  of  the  seventh  and  its  inversions  in  all  keys. 

§62. 

DECEPTIVE  PROGRESSIONS  OF  THE  DOMINANT  TRIAD 
AS  A  SUBSTITUTE  FOR  THE  DOMINANT  CHORD. 

When   the    dominant   triad   represents    the    chord   of  the 
seventh,  and  is,  in  consequence,  bound  to  its  resolution,  diver- 
gent  progressions   of  the   same   must   also   be  considered  as 
deceptive  progressions. 
298.  I  :$:        Wagner.  (Tannh.)        From  same. 


^ 


i 


In  the  last  example,  the  sixteenth-note  a  of  the  first  mea- 
sure is  an  anticipation. 

§63. 

DECEPTIVE  CLOSE. 

A  deceptive  progression  is  called  a  deceptive  close,  when 
it  takes  the  place  of  a  close. 


299. 


.<5>H^ 


1       I     J       1  I 

i— 1^— ^— •-r-W- 


f^^ 


m 


SM 


2^ 


tr^t 


-^• 


^'r^ 
^ZS 


^ 


^1    ^>      -g r-6'- 


I         I 


--piliEEs 


a 


.^ 


t 


m 


^ (52- 


:^ 


he; 


The  deceptive  close  of  the  dominant  chord  to  the  triad 
on  the  sixth  degree,  shortly  before  the  actual  close,  is  specially 
frequent  both  in  major  and  minor.  fNo.  293,  first  and  last 
examples). 


—     175     — 

§  64. 

DECEPTIVE  PKOGRESSIONS  OF  THE  OTHER  DISSONANT 
PRINCIPAL  CHORDS. 

As  the  deceptive  progressions  of  the  other  dissonant  prin- 
cipal chords  are  effected  in  precisely  the  same  manner  as 
those  of  the  dominant  chord,  they  may  all  be  comprehended 
under  a  single  exercise  with  subdivisions  and  examples. 


Exercise  45. 

Form  deceptive  progressions  from  one  key  to  all  others, 
with  fundamental  chord  and  inversions 

I.  Of  the  major  chord  of  the  ninth: 
300. 


^ 


-&- 


changing- dom. 


&^r7 


-G- 


ZZ. 


iiiiatetfiaa 


II.  Of  the  minor  chord  of  the  seventh; 
301. 


apappsggj 


-gnri^TPZ 


changing- dom. 


i^iearsaa^gf^ 


III.  Of  the  minor  chord  of  the  ninth: 


302. 


z=gpm^:^3 


^^^'- 


I 


changing- dom. 


5-— 6» 


-^ 


I 


^^% 


^«, 


fgggipiijSJ-^ 


—     176     — 


IV,.  Of  the  diminislied  chord  of  the  seventh; 
303. 


G- 


g~tyg 


ISE 


m 


i^e 


^^=^ 


s^ 


?.Efefe|;#Ji^- 


g^ — T 


changing-dom. 


s^Z=U-lCI^ 


(I^P^^El^^ggg^j 


i^^fepi 


* 


..-^    •«>■ 


•«»-  .•«- 


Mgj] 


V.  Of  the  diminished  triad: 

304. 


^ 


-G—9&- 


-^^3s^ 


changing-dom. 


^ 


^i=g: 


22: 


Qs: 


^ 


w 


^ 


Special  attention  must  be  called  to  two  deceptive  pro- 
gressions,' namely,  that  of  the  dominant  chord  (usually  5)  to 
the  chord  of  the  I  of  the  most  nearly-related  key  in  the  Circle 
of  Fourths;  e.  g.:  the  dominant  chord  in  G^-major  to  the  chord 
of  the  4  in  C-major: 


305. 


I    2   f 

and  that  of  the  diminished  chord  of  the  seventh  (usually  fun- 
damental chord,  sometimes  5)  to  the  chord  of  the  I  of  the 
most  nearly -{ elated  key  in  the  Circle  of  Fourths;  e.  g.:  the 
diminished  chord  of  the  seventh  in  ^- minor  to  the  chord  of 
the  I  in  C-major  or  c-minor: 


806. 


^gg:(^B 


^# 


m 


■fe 


177     — 


Or  else: 

307. 


i^gaiS 


=t 


* 


I 


I  h 


Sometimes  the  diminished  seventh,  when,  followed  by   a 
major  chord,  is  written  as  a  major  sixth: 

I         .  ,  I    etc. 


308. 


:^=i^ 


-A^ 


S' 


-4^-H^ 
i^^ 


f 


Both  deceptive  progressions  are   of  daily   occurrence  in 
modulatory  phrases  and  cadences. 
Cadence. 

4 J- 


309. 


I 


rJ      .,^ 


m 


rJ        rj- 


-(O. ,a_ 


f-f 


i 


^ 


:f=U 


9i 


e 


^=qr=^=^ 


t==t 


Both  are  customarily  designated  as  cJianging- dominant 
progressions,  because  the  dissonant  chords  belong  to  the  domi- 
nant of  the  dominant,  the  so-called  changing- dominant. 

§  65. 
SEQUENCES  WITH  DECEPTIVE  PROGRESSIONS. 

Any  deceptive  progression  may  be  made  the  motive  of  a 
sequence. 

310- J^)  etc.    ft.)  etc. 


W^^^^^^ 


a 


^S^Sii^ii^^^ 


9fc 


\i^ 


■i9-    ■<$>•  5.:^- 


i^e^j^^^- 


^^^ 


(c) 


(9 


ia: 


etc. 


etc. 


^=tls_l     ^_te 


^. 


.■zserrtZT-E: 


T' 


l^btt^ad^g: 


fe 


I-     o     Pg^i    g     )gy 


^5^rrJ!2=-.^=izi^=fi 


B  ussier.  Elementary  Harmony 


12 


—     178     — 

In  like  manner  combinations  of  yarious  deceptive  pro- 
gressions, by  themselves  or  with  other  added  modulations, 
may  serve  for  motives  of  sequences. 

311.  etc. 


etc. 


etc. 


^^^^^^m^ 


ff^ 


^r 


T  r 


J: 


i*       I     I   Jfi£ 


^S^-iS^ 


t^Vrm^^ 


^^^P# 


g^^^^^gj^^^ 


Exercise  46. 

1.  Form  sequences  with  these  and  similar  simple  and 
compound  motives,  particularly  according  to  No.  310 ce,  6, 
with  the  descending  chromatic  and  enharmonic  scale. 

2.  Form  modulatory  phrases  with  regular  modulations 
and  deceptive  progressions,  tone-repetitions  and  cadences 
with  deceptive  progressions.  Harmonize  the  ascending  and 
descending  melodic  minor  scale. 

3.  Harmonize  the  following  melodies,  which  give  00- 
casion  to  employ  deceptive  progressions. 


179     -- 


213. 


^=F=f-1J^E^g^^EiEz-^Sg^ 


214. 


i^ 


-f9- 


W=^t 


^ 


|S 


Ei^ 


^m^. 


|^E^r:tff?J-^,^fegl^^^^ 


§66. 
DECEPTIVE  PKOGRESSIONS  OF  THE  SUBORDINATE 
CHORD  OF  THE  SEVENTH. 
The  regular  progression  of  this  chord  leads,  as  we  arc 
aware  (§  28),  either  to  a  dissonant  principal  chord  or  to  the 
dominant  triad,  or  to  the  chord  of  the  %  of  that  key,  upon 
whose  second  degree  it  stands;  it  is, therefore, limited  to  pro- 
gressions to  certain  fixed  chords.    We,  consequently,  reckon  the 
progressions  of  tliis  chord,  as  well,  io' other  chords  besides  the 
above,  to  the  deceptive  progressions. 

These,  like  those  of  the  dissonant  principal  chords,  are 
the  more  easily  effected,  the  greater  the  similarity  is  between 
the  irregular  and  the  regular  progressions;  the  least  easily, 
when  the  seventh  is  obliged,  contrary  to  its  nature,  to  progress 
by  a  step  upward. 

To  gain  a  proper  conception  of  the  following  examples, 
it  is  necessary  to  strike  the  tonic  triad  each  time  before  the 
subordinate  chord  of  the  seventh. 
312. 


^^Spfe^^^SS^S^^P 


^iz^^ 


.^_<22. 


IE 


-7^--<9- 


\f^     .vv| 


■<g-b/ 


J^^ 


-g*— (g-[7:^-->6»-6>- 


12  = 


—     180     — 


Modulate  to  minor  similarly.    The  above  examples  always 

choose  the  way  through  a  dissonant  principal  chord,  by  pref- 
erence the  dominant  chord.  In  the  last  example,  the  trans- 
formation of  the  subordinate  chord  of  the  seventh  in  c-minor 
to  the  minor  chord  of  the  seventh  in  j^?-majpr  led  directly 
into  the  triad  of  this  latter  key.  Of  course,  progressions  to 
the  subordinate  chord  of  the  seventh,  or  the  chord  of  the  2  in 
other  keys,  are  also  practicable. 
313. 


^^^}^ 


:(S)^ 


-r? — <9-^ 


(8)' 


^=^=^' 


.f^=2^; 


m 


gE 


n-g-^-y, — -w^bfi? 


g^^Pi 


Deceptive  progressions  with  the  subordinate  chord  of  the 
seventh,  in  sequences: 


r  r  r  ff  f 


akU.^i--,.xi.j!dfeEfegfete 


J=sJ=J 


^1^1 


eta 


It  may  also  be  observed,  that  there  are  modulatory  pro- 
gressions of  the  4  chord  nearly  related  to  the  deceptive  pro- 


—     181 


gressions,  by  reason  of  the  peculiar  tendency  of  the  J  chord 
to  certain  progressions  (§  13);  e.  g.: 

315. 


I 


terf 


i-tj- 


-^ 


n 


^ 


:^3=g 


-SI 


rrr-r-r 


iE^^ 


I    I 


ZC 


^&# 


9fc 


•— ^ 


^^ 


£^ 


^^^g= 


i 


f 


£ 


^;^ 


Exercise  47.  I. 

Form  deceptive  progressions  with  the  subordinate  chord 
of  the  seventh;  likewise  sequences  and  modulatory  phrases 
in  which  this  chord  is  employed. 

§  67. 
THE  OTHER  SUBORDINATE  CHORDS  OF  THE  SEVENTH. 

The  subordinate  chords  of  the  seventh  on  the  first,  third, 
fourth,  and  sixth  degrees  are  classed  among  chords  containing 
both  harmonic  and  foreign  tones,  and  are  treated  as  such 
according  to  §§  40  and  44. 

They  usually  resolve,  one  into  the  other,  in  such  a  way 
that,  above  a  bass  progressing  in  diatonic  fourths  and  fifths, 
the  third  of  each  chord  becomes  the  seventh  of  the  next. 


316.  continued 

p   ^  tt       ft  ft      t   t 


^EE 


-&—&- 


—     182 


We  obtain  this  progressive  chain  of  dissonances,  which  is 
also  used  in  inversions,  by  divesting  Sequence  No.  310 


317. 


(I 


-^■=s.% 


WP-K, 


=i^^g|P8^ 


--^'ZL 


i- 


etc. 


=^ 


:l2^ 


of  all  chromatic  signs. 

Subordinate  chords  of  the  seventh  combine  with  diatonic 
triads  in: 

t 


^^^^^E|E 


318.     <^ 


At  t  the  diminished  triad  is  treated  like  a  consonant 
chord,  this  appearing  justifiable  here  in  view  of  the  consistent 
leading  of  the  parts. 

Exercise  47.  II. 

Form  progressions  like  tlie  above,  also  with  inversions. 

These  chords  also  afford  opportunity  in  another  way  for 
a  diatonic  interlocking  of  dissonances,  occurring  with  peculiar 
frequency  in  the  works  of  the  contrapuntists  (Lotti,  Bach, 
Handel),  and  among  the  moderns  with  Mendelssohn.  Here  the 
resolution  of  each  dissonance  produces  another: 


319. 


*^  2  7  6 


i? 


^3^iiEgiE 


2  7 


etc. 


Such  series  gain  greater  variety  by  the  occasional  entrance 
of  a  modulation  or  change  of  mode. 

Subordinate  chords  of  the  ninth  also  occur  in  like  series 
although  soldo mer.    An  example,  in  which  diatonic  chords  of 

the  seventh  alternate  with  subordinate  chords  of  the  ninth,  occurs 
in  the  Finale  of  Mozart's  great  symphony  in  C,  (called  ''Jupiter"), 


—     183    — 


320. 


=^' 


^ 


S^Ei 


m 


P^ 


This  passage,  of  which  a  mere  harmonic  skeleton  is  given 
here,  is  made  still  more  dissonant  by  the  passing -tones  of  a 
two-part  imitation  and  the  doubling  of  the  ninth  below  (which 
is  forbidden  in  Elem.  of  Harm.  §  133,  and  here  in  §  9). 

The  suspended  chords  of  §  40,  and  all  related  combina- 
tions, may  take  part  in  modulatory  treatment  and  deceptive 
progressions,  being  then  usually  included  under  the  conception 
of  a  change  of  Tcey  during  the  resolution  of  the  suspension. 


Chord  of  the  11th. 


Chord  of  the  13  th. 


321. 


._^- 


l5L=gJ^=:feg— 


.Ct ^Q. 


C.  Progressions  of  Triads. 

§  68. 

The  direct  succession  of  remote  triads  ~  which,  before 

the  era  of  the  sovereign  key,  resulted  quite  naturally  from  the 

leading  of  the  parts,  and  has  in  modern  times  been  frequently 

employed  for  special  artistic  ends  —  can  here  be  no  object 

for  practice,  but  merely  one  for  remark.     Below  are  a  few 

examples,  which  might  easily  be  multiplied  by  examples  from 

the  works  of  modern  masters. 
322. 


—     184     — 


^— f 


m 


s 


Beethoven. 


i^ 


-fej,-^j-i 


-<9<S>- 


f=^ 


Liszt. 


I 


=^^-jr 


-<2 ^_ 


^1 


fiTtr^-i* 


:r=k 


^m 


:^- 


-K 


§  69. 


CHORD-PEOaRESSION  AND  MODULATION  INDEPEN- 
DENT OF  THE  LEADING-  OF  THE  PARTS  AND  THE 

MELODY. 
To  effect  parallel  motion  in  all  parts,  or  in  as  many  as 
possible,  taking  solely  into  consideration  the  avoidance  of 
parallel  fifths  and  octaves,  we  form  series  of  chords  of  the 
sixth,  diminished  chords  of  the  seventh,  etc.,  in  diatonic,  chro- 
matic, or  mixed  progression. 


323. 


I 


^ 


^ 


J-  i  a 


f^^'^ 


i 


n. 


f 


t=t 


i 


iiiij 


^ 


j^-ui 


etc. 


II..  I  I      I  I 


—     185     — 


/iQ      I     J  J      l-ul.J_l     J- 


II  III!  etc. 


91 


-b. 


U 


F^- 


iiii 


The  fourth  part,  added  to  the  first  two  series  of  chords 
of  the  sixth,  may  easily  be  felt  as  a  disturbing  influence  through 
its  opposition  to  the  smooth  parallel  motion  of  the  remaining 
parts,  for  which  reason  these  progressions  are  preferably  em- 
ployed in  three  parts. 
324.    Progressions  in  contrary  motion.  


and  reversed.  ■  a  etc 


m 


^ 


reversed. 


fcbS=iti 


The  following  harmonic  leadings  also  result  from  the  pro- 
gression of  all,  or  the  separate,  parts.  Some,  it  is  true,  may 
be  harmonically  explained  in  another  way.  For  the  course 
of  composition,  and  the  composer  as  such,  it  is  indifferent, 
which  explanation  deserves  the  preference.  Kesearches  in  this 
connection  are  left  to  the  Science  of  Music,  which  undertakes 
to  solve  as  problems  precisely  those  things,  that  the  Theory 
of  Composition  takes  for  granted  as  the  right  of  musical  talent. 
(Comp.  Introduction). 

(a)  Bach.  (b) 

4—. ^ — ■ i H-, 1 [ 


325.  < 


I 


S 


|jr 


i 


*r 


m 


s 


>-k 


f^^^n^^^-^^Ft^r^^^ 


—     186     — 

(c)    Liszt,    (Harmonic  sketch.)  (d)    Mozart. 


•iii  i 


e^ 


-f9- 


gpE 


F^^ 


jO. 


I 


s 


m 


V 


I     L     I 


O- 


# 


F^F^^^^^T 


->5^- 


-iSt—ii^ 


i^U:l 


-8r- 


t 


f 


£ 


t--: 


-f 

(a)  Here  the  semitonic  progTession  of  all  parts  leads 
directly  from  the  J.-major  triad  to  the  dominant  chord  in  E^, 

(b)  Here  the  degree  wise  progression  of  all  parts  results  in 
a  similar  combination  of  apparently  remote  chords.  But  the 
chord  f-a-c-elf  is  here  only  a  passing  form  between  e-g-b 
and  d-f-b. 

(c)  Progression  of  triads  and  I  chords,  induced  by  the 
leading  of  the  outer  parts. 

(d)  Here  both  chords  belong  to  the  same  key  (c?-minor) 
as  dominant  triad  and  subordinate  chord  of  the  seventh  on 
the  fourth  degree.  Their  progression  results  from  the  degree  wise 
leading  of  the  parts. 

The  other  examples  may  be  explained  in  like  manner. 

Another  peculiar  manner  in  which  the  melody  governs 
the  harmony  must  here  find  mention.  It  sometimes  happens 
that  the  melody,  or  a  part  of  the  same,  is  repeated  at  an 
interval  of  one  or  more  degrees  higher  or  lower  than  the 
original.  As  a  rule,  such  repetitions  require  exactly  similar 
repetitions  in  the  harmony,  as  a  contrary  treatment  would  be 
opposed  to  the  character  of  the  melody.  In  order  to  carry 
out  this  similarity  the  rules  of  harmony  may.  In  case  of  ne- 
cessity, be  disregarded.     For  instance,  the  following  melody 


—     187     — 


326. 


literally  repeats  the  first  four  measures  a  whole  tone  lower, 
and  requires  a  like  treatment  of  the  harmony,  despite  the 
direct  succession  of  the  D-major  and  /"-minor  triads  caused 
thereby. 

327. 


^f^^^fsm^^^^ 


^=^.kd^^=J=^ 


luJ         I 


•75I5 


-^: 


A 


* 


t 

After  performing  these  eight  measures,  a  continuation  with 
the  el^-mmoY  chord  would  appear  quite  natural,  because  c[?-minor 
stands  here  in  the  same  relation  to  the  preceding  C-major,  as 
/■-minor  above  to  D-major,  and  the  ear  is  thus  prepared  for 
this  progression. 

7-h7SlTT-KJ      J    I       I      J      ^    I    <g       J    I        I     I    -f 


P 


^Ef^^^^^p 


3 


i 


iSi 


'All 


I  J 


g^ 


J. 


I        I 


=^ 


fe 


— <$>- 


^ 


-<5»- 


§  70. 


EMPLOYMENT  OF  FOEEIGN  TONES  IN  MODULATION. 

Hitherto  we  have  had  only  occasional  opportunity  for  em- 
ploying foreign  tones  in  modulating.  Melodies  for  practice 
now  follow,  which  are  abundantly  supplied  with  modulations 
and  foreign  tones.  After  the  insti-uction  given  in  Part  II,  all 
further  information  needed  can  be  gathered  from  the  following 
example. 


—     188     - 

Exercise  48. 
Work  out  in  four  parts  the  following  melodies,  which 
contain  modulations  and  foreign  tones.  The  pupil  is  of 
course,  at  liberty  to  lend  more  variety  to  the  lower  parts,  and 
to  fill  out  the  rests  harmonically,  by  employing  foreign  tones; 
but  he  is  cautioned  expressly  not  to  overload  the  harmonies. 
Each  of  the  following  melodies  can  be  worked  out  in  various 
ways,  and  it  is  advisable  to  do  this  in  some  cases,  at  least. 

Model  36. 


m 


p 


N=rt 


i 


^^a#^# 


f^ 


If 


m 


h:LllA:iL=i 


ifejjag^=^-i 


^  ^  ^    P 


s--^ 


I 


k=i^:  -'i  r:J5j5 


4' 


-0—0- 


^m^^m 


f==f 


J4 


ilAll  J 


»^yr-r^7-r-^=N#^ 


f=^f 


215, 


—     189     — 
Examples  for  Practice. 


216.    Moderato. 


^^^^gi^-^^^^ 


t-^^g^^^^E^^ 


m 


liipfp^feE^ 


217.    Allegro  moderato. 


^^^^^^^^ 


^^^^^^^^^^^^^^ 


teEE 


:i=f=»=i: 


»-r  p  »- 


^ 


:t=^=t 


i 


U— i»-»-p: 


—    '    '    ' — i^ — 


219. 


tE^^St^ 


^ 


^^^^^^^^^^ 


P^^^i^^^^ 


i^^^i^gli^lggS^^^^ 


—     190    — 


^^^^^^^^^^^^ 


221. 


S^ 


i3=^ 


I — ^-^ 


^^gi 


br-.^ 


i2^=i^^ 


w 


:t=t: 


i 


iEfe 


^ 


PP=PF 


t=4: 


-/»- 


-^t 


i^ 


^i^ 


I 


222. 


^— •^•z^v-=^ 


f^-*- 


^2/_,. 


1=t: 


E@[i^ 


~»—d 


i 


^•-r-^^.z=p: 


t=t 


S 


1=^ 


223. 


i=i 


&« 


atjsi: 


::1=: 


-<5»- 


F^M^g 


^^=fn-^s 


tx 


pm^=rf=m=^=^=^^^ 


^f^^.=anlgs^»f=hr^-=^ 


^ 


« 


224. 


s 


-^ — •- 


^^ 


:r-t^i — I — r-t 


-«s>-  ■•■ 


P^^^^^^^Sfe^^S 


41 


^^^^^^^^^^^ 


^ 


FP^s^^^^ii 


:=^ 


s^" 


—     191 


225. 


«-B^E^ 


#=p: 


^3 


:?=P= 


^S 


#i 


a^i^^ 


t=\^ 


ir^^ 


-t-=^ 


-G-Y 


^ 


226. 


E3 


?^i|^^ 


?=lEE 


^^^^=1 


t==:t 


^^^^i^5^|^^^|^^|^:^Pg| 


227. 


[^ai^^^^^s^i^s 


^^^ 


!?-^ 


i^i^ 


^?=¥=^ 


1 


^^^» 


:?=c=^: 


^^ 


^^ 


Sf^ 


ttl?p=B£ 


5^=?: 


;feiH?= 


^^^m 


gESEEsEE^H^^ 


0 


:s: 


.o^T" 


—     192     — 


IV.  The  Altered  or  Mixed  Chords. 

§  71. 
EXPLANATION  OF  THE  TERM. 

All  chords  as  yet  learned  were  composed  of  the  tones  of 
a  single  major  or  minor  key,  and  were  affiliated  with  the 
same.     Such  chords  are  therefore  called  diatonic. 

Those  chords,  on  the  conti-ary,  which  cannot  be  foimed 
with  tones  of  that  key  with  which  they  are  affiliated,  are 
called  mixed  chords.  This  term  is  founded  on  the  idea,  that 
they  are  composed  of  tones  belonging  to  different  (and  thus 
mixed)  keys.  They  are  also  called  altered  chords,  as  arising 
from  diatonic  chords  through  the  (chromatic)  alteration  of  single 
intervals. 

In  practical  music,  such  harmonic  combinations  are  considered 
as  resulting  from  foreign  tones,  chiefly  passing-notes  and  suspen- 
sions. Some  of  them,  on  account  of  their  extremely  frequent 
employment,  are  to  be  distinguished  and  used  in  j)ractice  as 
individual  chords  ;  namely  : 

1.  The  chord  of  the  sixth  derived  from  the  subordinate 
triad  on  the  flatted  second  degree  in  minor; 

2.  The  augmented  chord  of  the  sixth; 

3.  The  augmented  tiiad. 

§  72. 

THE  SUBORDINATE  TRIAD  ON  THE  FLATTED  SECOND. 

We  have  long  been  familiar  with  cadences  formed  with 
the  sub-dominant  triad  and  the  subordinate  triad  on  the  second 
degree,  chiefly  in  its  first  inversion.  In  minor  the  ti-iad  on 
the  second  is,  as  we  know,  diminished. 


—     193    — 


329. 


9i 


=g: 


t=t 


t=:1: 


M 


If  (in  minor)  a  minor  sixth  be  suspended  with  the  sub- 
dominant,  or  brought  in  as  a  chromatic  passing-note  in  the 
highest  part  with  the  subordinate  triad, 


330. 


* 


1=t 


-^- 


mm^^m 


T 


^i: 


^ 


P^l 


there  will  result,  as  at  f ,  the  chord  of  the  sixth  of  a  major 
triad  h\>-d-f^  which  we  call  the  triad  on  the  flatted  second, 
because  it  presupposes  the  flatted  second  of  the  key  (here  &> 
in  a-minor)  as  its  fundamental.  In  this  first  inversion  it  enters 
independently  in  all  cadence -like  progressions  instead  of  the 
sub-dominant  triad  or  any  substitutes  for  the  latter.* 
331. 


^^^^1^^ 


(9— 


Beethoven. 


P 


Ebl 


r 


^il^^irai 


i^3? 


SS 


I  J     I 


S2i 


f 


-g*- 


Ei 


n 


il 


*   As   a   peculiarity   of  the  school  of  the   celebrated  Neapolitan, 
Scarlatti,  it  was  named  the  "Neapolitan  chord  of  the  sixth". 
B  ussier.  Elementary  Harmony.  13 


194     — 


332.    (a) 


'at — s,. 


^m^ 


^^^^ 


f,^ 


s 


E^ 


-^ 


At  ('a^  we  see  an  oft-recurring  and  harmonious  form  of 
the  half-close  with  interpolated  diminished  chord  of  the  seventh; 
at  (h)  the  same  with  suspensions. 

The  root -chord  itself,  instead  of  the  chord  of  the  sixth, 
seldom  occurs;  the  4  chord  by  way  of  exception,  and  with 
the  succession  (here  forbidden)  of  two  4  chords. 

J — V 


333. 


^^^ 


-^^ 


t=X- 


^ij^i^i 


i^i 


m 


gj^^m^ 


^ 


E^:^=F 


i 


Like  other  sub -dominant  chords  originally    belonging  to 

the  minor  mode  it  is  also,   although  seidomer,   used   in   the 
major  mode. 

334.  1..  2. 


^ 


f 


bid: 


J 


:7^.d 


tetiSt 


'^TT"r 


^ 


I 


m 


i 


«d 


-«-k- 


t=F 


*f: 


S=fc 


n — T 


i 


1 


—     195     — 


Explanation. 

1.  The  ^1?- major  triad  enters,  as  subordinate  triad  on 
the  flatted  second,  directly  after  D-major,  and  leads  similarly 
back  to  the  same,  precisely  like  the  regular  diatonic  triad  on 
the  second  degree. 

2.  The  same  chord  enters  here  in  like  manner,  but  is 
regarded  and  treated  like  a  true  jEJl^-major  chord,  thus  afford- 
ing opportunity  for  a  direct  connection  of  -El?- major  with 
D-major. 

3.  Here  the  JE'l'-major  triad  is  again  regarded  as  a  sub- 
ordinate ti'iad,  and  shortly  led  back  to  D-major. 

As  a  substitute  for  the   sub-dominant,   it   may   alternate 
with  the  other  substitutes  of  that  chord.    A  brilliant  example 
from  Beethoven  follows; 
335. 


Explanation.     Cadence  in  JE't?- major.     In  measure  5   our 
subordinate    triad   takes   the   place  of  the  subordinate  chord 
of  the  seventh,  and  leads  through  the  dominant  triad  to  the 
tonic  triad. 
336. 


—     196     — 

1.  Here  the  direct  succession  of  cjj-minor  and  C-major  is 
justified  by  tlieir  similar  relation  to  ^-major  as  the  substitute 
for  the  sub-dominant. 

2.  Same  relation  of  6 -minor  and  5b-major  to  ^- major. 
N.B.    The  works  of  the  last  two   centuries  exhibit  innu- 
merable examples. 

Exercise  49. 

1.  Form  cadences  with  this  chord  in  the  customary 
15  minor  keys  and  also  in  ej},  6j},  d\f,  and  f/t?-minor. 

2.  Harmonize  the  following  melodies. 

Model  37. 


m 


3 


m 


C^STTT 


#^«^#- 


-r-f 


§5 


,^.     J  J  /-^j^-j 


I^i 


P^ 


^ 


flF 


^^^^^ 


■ 


m 


i 


r 


m 


^^ 


—     197     — 


Explanation. 

1.  Passing-note  in  two  parts. 

2.  Deceptive  close. 

3.  Deceptive  progression. 

4.  The  D- major  chord  obtained  by  the  deceptive  pro- 
gression is  regarded  as  the  triad  on  the  flatted  second  in 
c  {(-minor,  and  treated  accordingly. 

5.  One  of  the  commonest  progressions  of  parts  or  triads, 
which  is  founded  on  §  26.  (Comp.  p.  169,  No.  288,  and 
§  168). 

6.  Here  the  (7- major  chord  obtained  by  modulation  is 
regarded  as  a  subordinate  triad  to  &-minor. 


228. 


Examples  for  Practice. 


SEBE^g^lfEf^ 


:«=t: 


-:S. 


jzfciiisz 


229. 


^^M 


l^E^ 


>*- 


■O      I  =« G~  -  ^         ^-^1- 


230. 


:9= 


^^'Tt^-T^^^ 


«F 


g^^^^Fr^T^ 


-t-^ 


rF^-^ 


i 


231. 

fe  6      s 


^=td=t:s 


P=i: 


#^#- 


1t^ 


^ii: 


lE>g^tJd^J=^ 


^^^^ 


*^ 


?^»-.-b^^^?=:iJv^ 


-•^ •- 


—     198     — 


§73. 

THE  AUGMENTED  CHORD  OF  THE  SIXTH. 

The  augmented  chord  of  the  sixth  is  conceived  as  resulting 
1.    From  the  chord  of  the  sixth  derived  from  the  minor 
triad,  by  a  chromatic  passing-note  in  the  highest  part: 


337. 


^^M 


2.    From  the  chord  of  the  sixth  derived  from  the  major 
triad,  by  a  chromatic  passing-note  in  both  outer  parts: 


338. 


F=«^ 


g=|g: 


3.  From  both  the  above  chords,  by  chromatic  passing- 
notes  as  under  1  and  2,  but  together  with  a  diatonic  passiug- 
note  in  an  inner  part: 


339. 


l^^^^^^ 


4.  As  above  under  3,  with  the  addition  of  the  perfect 
fifth  as  a  fourth  ("filling-up")  part: 

340. 

5.  From  the  chord  of  the  sixth  derived  from  the  dimin- 
ished triad,  by  a  chromatic  passing-note  in  the  lowest  part: 


341. 


VS'- 


6.    From  the  5  chord  derived  from  the  diminished  chord 
of  the  seventh,  in  like  manner: 


342.    ^§Eg^<Etep^ 


7.    From  the  t  chord  derived  from  the  dominant  chord, 
in  like  manner: 


343. 


i^^ 


—     199     — 


8.   From  this  latter  augmented  chord  of  the  sixth,  by  the 
double-augmented  fourth  taken  as  a  passing-note: 


344. 


It  therefore  occurs  in  four  forms: 
345. 

with  major  third  and  augmented  sixth, 


with  major  third,  perf.  fifth,  and  augmented  sixth, 

with   major   third,   augmented  fourth,  and   aug- 
mented sixth, 

with  major  third,  double-augmented  fourth,  and 
augmented  sixth. 


is 


■n 


In  the  second  and  fourth  form  it  is  regularly  led  to  the 
4  chord;  in  the  third,  to  the  dominant  triad,  or  seldomer  to 
the  I  chord.  Thereby,  the  two  parts  forming  the  augmented 
sixth  resolve  degreewise  in  contrary  directions.  The  tirst  I'orni 
can  employ  both  progressions. 


346.  I       I  .  I      , 


-^ — # — •- 


(9- 


^ 


=Jfe=  = 


^ 


5^ 


m 


\-r-4- 


<5> [-~f9 


^ 


-¥ 


1 


1 


J 


tts: 


iS 


i 


^ 


*  The  two  chords  indicated  here  fill  out  each  of  the  first  fouf 
examples  to  a  complete  cadence. 


—     200     - 


The  foregoing  cases  prove  that  the  augmented  chord  ot 
the  sixth  by  far  most  frequently  employed,  is  that  formed 
on  the  second  degree. 

It  resolves  extremely  seldom  to  the  minor  triad. 


347. 


8g= 


^s^ 


f 


J    J 


t=t: 


?^='6>" 


m 


It  is  then  to  be  formed  on  the  flatted  second  degree,  and 
arises  from  the  alteration  of  a  diminished  triad,  dominant  chord 
of  the  seventh,  or  the  \  of  the  diminished  chord  of  the  seventh. 

The  augmented  chord  of  the  sixth  is  by  far  most  fre- 
quently employed  in  the  cadence  instead  of  the  sub-dominant, 
and  in  half-closes  (Nos.  346,  348). 

The  higher  parts  of  the  augmented  chord  of  the  sixth 
can,  of  course,  be  transposed. 


1-^ 


e 


Root-chord,  and  inversions  of  same. 

By   going   back   to   the   fundamental   forms   of  the   aug- 
mented chord  of  the  sixth  we  obtain: 

349.  ^    ,  ^  

a  diminished  triad  with  diminished  ["/ 

Efe 


from 


Si 


m^'^ 


from 


from 


third;  ^^^. 

350.  ^ 

=^^  a  diminished  chord  of  the  seventh  P^ 

with  diminished  third;  ^W~^^ 


m 


— ^  a  dominant  chord  of  the  seventh 
with  diminished  fifth. 


^^ 


201     — 


These  occur,  in  works  of  this  and  the  last  century,  both 
in  the  forms  of  sub-dominant  and  of  dominant  chords  (again 
by  far  most  frequently  in  the  former),  but  very  seldom  in 
comparison  with  the  augmented  chord  of  the  sixth  itself. 
Inversions  of  the  augmented  chord  of  the  sixth,  or  rather  of 
its  root-chord,  are; 


352. 


These,  as  well  as  the  root-chords,  are  preferably  employed 
where  the  inversion  of  the  augmented  sixth  to  a  diminished 
third  is  avoided;  though  they  also  occur  in  this  form. 


853. 


^Efe 


m 


^ 


=TptJ 


<9- 


(9- 


gj^gji^a^^ia 


Enharmonic  changes. 

The  three-part  augmented  chord  of  the  sixth,  and  that 
with  the  perfect  fifth,  may  be  enharmonically  transformed  to 
an  incomplete  and  a  complete  dominant  chord  of  the  seventh: 


^-  lm&^  "''^''  S5^i 


through   which   means   keys  appear  nearly  connected,  which 
are  removed  from  each  other  by  5  or  6  degrees  of  affinity: 


355. 


—     202     — 

At,  D 


EEfEiiE/g\EaS;^ 


r 


g^j|j^\^/^^^|^^ 


We  were  already  acquainted  with  similar  transitions  as 
deceptive  progressions  of  the  dominant  chord  (No.  295  [2,  3]; 
No.  311).    Here  they  result  from  enharmonic  changes. 

The  third  form  of  the  augmented  chord  of  the  sixth  (with 
augmented  fourth)  may  be  enharmonically  transformed  into 
the  root- chord  of  another  augmented  chord  of  the  sixth  of 
like  kind. 

n 


356.     <^ 


p-- 


^^^^^^^\fj^. 


Deceptive  progressions 

of  the  augmented  chord  of  the  sixth  are  formed  according  to 

familiar  rules: 

Mozart. 


357. 


^=^: 


\p^^^^^^^ 


Combined  with  foreign  tones 

358.   Wagner,  "  Tristan. 


rzi 


^^ 


5fc 


—     203     — 


Exercise  50. 

1.  Play,  with  the  augmented  chord  of  the  sixth,  four* 
part  cadences,  modulations,  enharmonic  and  deceptive  pro- 
gpessions,  sequences,  and  modulatory  phrases,  always  fixed  by 
retaining  the  augmented  sixth  (i.  e.:  avoiding  the  diminished 
third),  and  by  preference  in  open  harmony  (this  facilitating 
observation  of  part-leadings). 

2.  Play  a  few  modulatory  phrases  containing  root-chord 
and  inversions  of  the  augmented  chord  of  the  sixth. 

3.  Harmonize  the  following  melodies. 


Allegro.  Model  38. 


m 


LAJ_1^ 


U 


t 


PE 


r 


I 


h 


^ 


i 


^ 


I 

jL 


frTr=r=^ 


f 


^ 


t 


kkLU  ftj  I  ^-^ 


t 


—     204     — 


^ 


^^fc=^j#U=feJ-HH 


r^ 


"J.  i 


5^ 


if 


(enharm.) 


I 


h=^^i 


m- 


j— J— *-g 


r 


Brr  I T  #-f-^ 


i?; 


-i« — pt — 1«- 


^^U^^^UM 


*y^p^^ 


i 


J #  t—±: 


^ 


/J  !ni 


^^^ 


#J 


^# 


e 


i=#E 


f 


m 


Examples  for  Practice. 
232.    Allegro.  - — -  f 


-^ — r 


I 


?=^=i?^==p=|»=T=p=^g=p- 


t,     t 


£5 


-fS2- 


^^e!^=^^i* 


-IP   »- 


:{={: 


—     205     — 


^yrr-^ 


233.    Andante. 


*=t 


gS^^^lf^ 


lfe 


f-rf-tii-b»f 


^ 


1*^ 


E|:3^^t:j?4i3^^ 


p^PrTrr^^F^i^^^^ 


234.    Adaqio. 


■»?- 


p|g^Fgigg^^-^^^¥?s 


i 


fes:i|iW=fe^ 


J^^^^l 


§  74. 

THE  AUGMENTED  TRIAD. 

The  augmented  triad  occurs  as  a  diatonic  chord  ia  minor 
(§  23).  In  this  capacity  we  conceive  it  as  resulting  from  a 
suspension;  as,  in  the  following  examples,  from  the  suspensions 
of  the  augmented  fifth  (g'f): 


359. 


\=W=^- 


m 


I,        g i^" 


:tJ 


t^m^. 


-J2L 


in  the  next,  from  the  suspension  of  the  fundamental  (c): 


len 


s; 


t=|g: 


360. 


^t 


i^... 


^ 


H 


is 


—     206     — 

As  a  mixed  chord  it  is  chiefly  developed  from  the  fifth 
of  a  triad  used  as  a  chromatic  passing-note: 


361.   < 


=j: 


m^^ 


l-4i4 


m^. 


m 


J' 


^ 


Enharmonically 

it  may,  by  reason  of  its  two  similar  intervals  (major  thirds), 
be  transformed  into  the  inversions  of  two  other  augmented 
triads. 


^^P 


P 


-gp         gy    — r>- 


Deceptive  Progressions 

are  obtained  according  to  familiar  rules.    E.  g.: 


363. 


m 


^ 


-?g — <g- 


^E^ 


s: 


In  the  cadence: 


364.     ^'^=^ 


W- 


JJS  7         I77  5  7 


—     207     — 


Exercise  51. 

1.  Play,  with  root -chord  and  inversions  of  the  aug- 
mented triad,  regular,  enharmonic,  and  deceptive  progres- 
sions, cadences,  sequences,  and  modulatory  phrases,  in  four 
parts  and  in  various  keys. 

2.  Harmonize  the  following  examples  for  practice. 

Model  39. 


m 


i- 


E^B=5 


flg;=^ 


rr — r 
i  J.    J    J 


[1 


U'M^ii.^ 


E 


* 


£ 


i 


:^ 


'rrrr — r 


aa^ 


-^- 


m 


?=PT 


1©- 


riUJrr^H^^ 


P-2 


fclS 


gsyy^ft-ft^ 


r 


r-r 


—     208     — 


235.     Andante. 

t 


Examples  for  Practice. 


^^^^^^t 


^- 


g^^ 


§  75. 
OTHER  MIXED  CHORDS  AND  SIMILAR  HARMONIES. 

Characteristic  leadings  continually  produce,  during  actual 
artistic  production  (i.  e.:  outside  of  mere  school-work),  new  for- 
mations of  this  nature,  which  are  treated  either  regularly,  i.  e.. 
in  accordance  with  the  original  harmonic  significance,  or  en- 
harmonically,  or  in  the  manner  of  deceptive  progressions. 

1.  In  the  following  example  we  see,  at  (a),  how  a  dom- 
inant chord  of  the  seventh  with  sharp  fifth  results  from  a 
passing-note  in  the  highest  part;  at  (h)  the  same  enters  hy  a 
skip,  at  (c)  as  a  link  in  deceptive  progressions;  at  (d)  it 
arises  enharmonically  from  a  dominant  chord  with  simple  sus- 
pension. 


365.    (a) 


U 


A 


(d) 


lE^^^SS 


&^l^^ 


yg6>- 


f 


,5^^ 


tf-Jta-r^ 


^E3= 


4=1 


2.    A  similar  chord,  though  bearing  a  quite  different  rela- 
tion to  the  key,  is  moulded  by  Schubert  as  the  last,  intensest 


—     209     - 


means  for  expressing  the  unbearable  burden  of  woe  of  world- 
bearing  Atlas.  Here  is  suspended,  against  the  continued  third 
and  fifth  of  the  ^-minor  triad,  the  flatted  second  of  the  key 
both  in  voice  and  pianoforte -bass,  the  voice  then  being  led 
through  the  seventh  of  the  key  back  to  the  triad,  while  the 
flatted  second  is  still  held  in  the  bass.  A  chord  is  thus  formed 
which,  considered  by  itself,  would  first  of  all  point  to  JEJb-major. 
In  this  the  pupil  has  one  of  the  most  striking,  as  well  as 
most  sublime,  instances  of  the  many-sidedness  of  the  chords, 
according  as  they  are  referred  to  one  key  or  the  other;  and 
likewise  of  the  manner  in  which  peculiar  harmonic  combina- 
tions arise  in  response  to  special  artistic  requirements. 
366.  .     Pn 


'^ 


-h 


^ 


3^ 


die    gan  -  ze  Welt  der  Sclimerzen  muss  ich  tra 


gen! 


P^ 


^ 


a 


^ 


Efe 


i 


t     l4.  =t  =t 


^^ 


i.  5  3  3  b: 


This  same  song  also  exhibits  still  other  harmonic  ti'ansi- 
tions  of  like  pregnant  significance. 

3.    Mozart   writes,    in    the    working-out    of   this    motive 

^  in  the  (5^-minor  symphony,  whose  first  tone 


367. 


Siit 


enters  nearly  throughout  as  a  suspension,  the  following  com- 
binations of  pure  four-part  suspensions,  marked  by  f. 


368. 


r^ 


J^N^ 


'0- 


ife^ 


!pSf'3 


i==i; 


^it^ 


Bnssler,   Elementary  Harmony 


—     210     — 


4.  Wagner,  in  his  cumulative  continuation  of  the  opening 
to  the  Tristan  Prelude  (given  at  end  of  §  73),  frames  a  freely- 
entering  harmony,  which  is  to  be  regarded  as  an  augmented 
triad  with  suspension  in  two  parts,  and  which  makes  a  decep- 
tive progression  to  a  dominant  chord  of  the  seventh  with  simple 
suspension. 


^^1^ 


The  tones  ^Jj,  d,  f,  represent  a  diminished  chord  of  the 
seventh,  which  combines  with  c  (tliird  of  the  key), 

§  76. 

ORGAN-POINT. 

Especially  toward  the  closo  of  emotional,  pregnant  com- 
positions, a  need  is  often  felt,  after  the  tonic  is  already  gained  and 
then  sustained  in  the  bass,  to  allow  the  movement  in  the  higher 
parts  still  to  continue  above  it — gently  to  expire,  so  to  speak — 
whereby  the  suggestiveness  of  the  close  is  enhanced. 

^™-     ■  J  j   J.  I   J, J  J-J 


^cid 


^ 


f-f- 


f 


-g^— ^- 


t22= 


m 


"r^^^r^r 


j  J.  1 J  J  I J  J  * 


'^^^^ 


ife£ 


'^- 


^ 


zi=XifL=r=.%z. 


I  J  '  i^J  1^ 


-     211     — 

A  similar  phenomenon,  as  a  preparation  of  the  close,  ia 
often  met  with  on  the  dominant,  where  all  the  parts  convene^ 
as  it  were,  to  celebrate  the  close. 
371. 


ir:^i^^^i#^ 


^fe 


The  tone  held  in  such  passages,  or  even  the  entire  pas- 
sage itself,  is  called  an  Organ-point  (Elem.  of  Harm.,  §  137). 

The  character  of  the  composition  often  demands,  that  the 
higher  parts  should  overstep  the  harmonies  and  modulations, 
which  stand  in  near  affinity  to  the  bass-tone  and  the  key  re- 
presented by  it. 


372. 


Through  the  aid,  in  particular,  of  the  chromatic  progres- 
sions exhibited  in  §  69,  which  might  in  part  be  termed  ap- 
parent modulations,  organ-points  gain  the  appearance  of  greater 
modulatory  variety,  even  should  these  progressions  not,  in  point 
of  fact,  overstep  nearly-related  harmonies. 
373. 


-^- 


¥ 


^ 


^^ 


^- 


f 


^ 


14' 


—     212     — 

The  sustained  tone  itself  may  appear  as  a  tone   oft-re- 
peated, or  interrupted  by  rests. 
374. 


y=^^^grj^qxm 


^ 

'l 


^^^ 


r  I 


J  i«ii^ 


^^^^^^^^^ 


# — &- 


Organ-points  are  also  found  at  the  beginning  or  in  various 
places  in  compositions. 

The  sustained  tone  may  likewise  appear  in  the  highest 
part,  or  one  of  the  inner  parts. 

Mozart.     (Harmonic  Sketch.) 


75. 


I 


fe^std 


I  .     I 


itns 


^ 


y  ^r  ^'^  p^it 


^fefey-f-W 


^?£3^S^ 


I 


\=^^ 


^^^: 


1==5 


:^iN 


^^1 


In  instrumental  music  the  organ-point  is  not  infrequently 
combined  with  foreign  tones;  comp.  Beethoven^  -4-major  sym- 
phony IV,  (7-major  sonata  Op.  2,  III,  coda;  Liszt,  JB-minor  so- 
nata p.  18,  meas.  319—327. 


Exercise  52. 

Form  organ-points  on  Tonic  and  Dominant: 

1.  restricting  modulation  to  nearly-related  keys, 

2.  witii  free,  but  carefully  considered  modulation. 


—     213     — 


§  77. 

MODERN  CLOSES. 

Foreign  tones  and  modulation,  especially  the  combinations 
of  triads  treated  of  here  in  §  28  and  illustrated  by  numerous 
examples  from  master-works  in  the  author's  "Partiturstudium" 
[Studies  in  Scoring],  produce  certain  modern  forms  of  the  close, 
which  appear  to  have  affinity  with  the  sub -dominant  close 
(pp.  34—35).  They  usually  follow  the  more  or  less  distinctly 
marked  dominant  close;  at  times  they  replace  it. 


276.   1. 


2. 


3. 


■^tt^-J — 1 — ^  -»'— ;d — ^--J  »J  /h^- 

^1  J  f-^-^^ — ^■-'^—f- — 

«?      k)    \       ^-H 

^=^ 


^m^m 


I        I. 

and  like  forms. 


25^ 


:s: 


a^ 


The  first  example  is  the  sub-dominant  close. 

The  second  example  was  mentioned,  as  regular,  by  Eameau, 
the  sub-dominant  being  represented  by  the  subordinate  chord  of 
the  seventh  II ;  ^  is  properly  a  passing-note. 

The  third  is  the  same  with  raised  b.  Here,  too,  f  might 
stand  for/ij. 

In  example  four,  the  third  c^  holds  its  own  against  the  sub- 
dominant,  thus  forming  the  subordinate  chord  of  the  seventh  IV. 

In  example  five,  only  the  f/jj  entering  by  a  skip  is  peculiar. 
With  a  sustained  in  bass,  and  d^  moving  degreewise  between 
repeated  e,  we  should  have  the  common  example  of  a  passing- 
chord  of  the  diminished  seventh. 


•       —     214     — 

In  example  six,  the  raised  dominant-fifth  combines  with  the 
minor  sub-dominant  third  to  form  an  apparent  ^-major  chord. 

In  example  seven,  e^  is  properly/,  and  the  thirds  of  the  tonic 
(cjj),  dominant  {g^),  and  minor  sub-dominant  (  f)  are  combined 
(§46). 

In  example  eight,  the  most  difficult  to  explain,  the  dominant 
is  held  throughout,  while  the  tonic  changes  mode  in  the  third, 
and  the  perfect  fifth  of  the  third  appears  as  a  passing-note. 

All  these  examples,  like  most  progressions  of  triads,  are  based 
upon  the  unreserved  (or  universal)  recognition  of  the  S3^stem  of 
equal  temperament,  whose  final  establishment  is  to  be  traced  to 
Bach's  *' Well- tempered  Clavichord." 

§  78. 
THOROUGH-BASS  NOTATION. 

The  exercises  with  thorough-bass  figuring  in  Part  I  noticed 
chromatic  signs  only  for  the  seventh  in  minor.  The  employ- 
ment of  modulation  naturally  calls  for  a  far  more  extended 
application  of  such  signs. 

Every  interval  taking  a  chromatic  sign  must,  as  before, 
be  noted  by  a  figure;  excepting  the  third,  to  which  any  in- 
dependent chromatic  sign  refers. 

Where  the  figures  are  crowded,  the  relations  of  the  chro- 
matic signs  might  easily  be  mistaken;  therefore, a  part  of  these 
signs  has  been  replaced  by  diagonal  and  perpendicular  strokes, 
which  combine  more  readily  with  the  figure,  and  indicate  that 
the  interval  in  question  is  raised  by  a  semitone,  thus  repla- 
cing the  jj,  X,  and  ^  respectively.  This  stroke  intersects  dia- 
gonally the  6,  7,  or  9  in  its  upper  or  lower  portion,  and  per- 
pendicidarljf  the  2,  4,  and  5;  or,  in  these  last  cases,  is  written 
directly  after  the  figure.  Thus  we  obtain  jg-,  ?,  9-,  2,  4,  6 
(2i,  4i,  5i).  No  similar  abbreviation  for  flatted  intervals  has 
come  into  use. 

Foreign  tones  are  also  noted  in  thorough-bass  figuring. 
But  thereby  not  only  the  reading,   but  also  the   writing,   of 


215      — 


foreign  tones  becomes  much  more  tedious,  than  even  the  wri- 
ting-out in  notes.  Now,  as  the  essential  advantage  of  thorough- 
bass notation  for  the  composer  consists  in  the  saving  of  time 
attained  through  the  same  in  sketching  or  fixing  a  musical 
thought,  the  theory  of  composition  has  nothing  to  do  with  a 
development  through  which  this  advantage  is  sacrificed.  Its 
study  shall,  therefore,  be  left  to  the  thorough-bass  player. 

Here  follow  some  melodies,  and  basses  figured  in  part, 
chiefly  intended  to  afford  practice  in  employing  deceptive  pro- 
gressions and  peculiar  harmonic  forms  (§§  69,  74).  The  pupil 
may  add  foreign  tones  at  will  to  the  figured  basses. 

Bach  does  not  figure  chords  of  the  eleventh  and  thirteenth 

7 

with  11  and  13,  but  with  |,  thus  disregarding  the  fifth  in  the 
former  and  the  sixth  in  the  latter.  However,  the  addition  of 
a  6  in  the  latter  case  would  appear  necessary,  when  figuring 
not  merely  for  accompaniment,  but  also  with  the  aim  of  fixing 
the  chords. 

Exercise  53. 

Employ  all  harmonic  material  in  forming  cadences,  har- 
monizing chromatic  and  enharmonic  scales  and  repeated 
tones,  and  modulatory  phrases. 

Work  out  in  four  parts  the  following  melodies  and 
basses. 

Model  40. 


t 


gpEp^ 


dAJ-il^i 


cj-'-^-fe 


8      tl5         2 


8      ^^         ^ 


216     — 


i 


^^^^m 


pf^-*f^f^ 


i  li 


6        41    '        '  '  '  h?  7  iJ 


6        41     ^       ^ 


i 


^^^^ 


f^f^ 


^^SMf 


*: 


S 


O  A  0  I 


6         7         6         41 


2        6 


237. 


it     i    *'    ^     j 

Examples  for  Practice. 


4        6 
3         4 


1—4—4- 


^^^^s^^^^^S^ 


ir=ijt=jizit2 


238. 


^ 


:^^ 


PS 


t 


tit 


«=*=3= 


aziJiij-jig^"^^^i^ 


6    X6  ~^Q      X6  6         6         i?6      flo      t^6      S^      feo    S^         6       7 


y9- 


239. 


^^ 


ES 


^ 


^ 


Organ-point, 


kti^ 


» d» 


I2ZS: 


—    217     — 


s 


^ 


:e3B3 


240.  . 


^m^^^^^ 


^^ 


1— -f^ 


s^ 


i±:=it 


2  « 


P5 


g 


P^fe^^ 


zzl^ 


:<9— ?g^ 


6       07 


;t!^t? 


6  6         7  7 

4  5         t] 


k  'Xwi 


4         6 


241. 


S 


6  tf  6 


^=fa=3 


^ 


23(-6* 


-«5>- 


9fc;=R3=: 


:^: 


4         7 

4         3         t! 


gi3 


•— ^ 


^ 


-^-•'— (^^ 


6         6         7 


«      6 —      517       i+ 


^=1^^^?^ 


^fc^fe«. 


•iZiztHt 


:1=:^ 


3 —      6         2  6  5  7  pa —  ^5         6, 

4  5/ 

242. 


8      6      4  6   h7 

8  5  "^ 


?^ 


^^^^^=^^^=^^m 


^^^^Bf^^ 


^^-FR^^r^^^ 


t=:t 


-?g^ — <g- 


-<5>- 


^^^^^g^5^^^^ 


^,rr-^r]i^^ 


e 


i:g; 


—     218     — 
245. 


5^ 


-^=is: 


:ps|^3 


riT-^^^^:!^ 


3l=:t: 


:te 


t^t 


Sirat 


:fe3i=t3*l=:;5-JEfe 


fe--tt 


^^s^i^^s 


i 


te 


^^ 


^« — • 


p— •- 


t=t 


:s^ 


246. 

•^  I       OrrrQn.-nniTif  I 


I     Organ-point 


P 


f 4 


t=^ 


(9 


■^ \- 


4-6? ff •- 


-^nrX 


o^ & — #- 


247.  £^w  ^oco  Allegro.    (Comp.  Nos.  326  to  328.) 


^^^^^^^E?^^_ 


-G— 


ra=* 


!«■ 


:?=i=if 


rt 


iE^;^93^Ep^ 


248. 


'^ 


^^3f 


t=5|: 


i^ 


;EEteti^?qtj: 


?^-f^^ 


249.   Allegro. 


^I^^^^^^^^^^^i 


=ra= 


^^:^^|^^ 


— a^ 


»— d 


^^^ 


--     219 


i 


»s* 


^ — • 


t=-t 


t=4: 


^=S=±i=j3- 


^ 


250. 


^^T^^^^^^^FF^^^ 


3^^ 


251.  Quasi  Adar/io. 


iP^^f^^^^jgjP^li^S 


g^qg-H-P^^^J^^^gffrl^F^^g 


i 


S^g+rt^^N^ 


3tZZt 


^^^^i^^^ 


Andante. 


M 


fli^= 


^ 


^  a 


H^^^S^^^piS 


,1=^=3: 


^ 


• •^ 


-• •- 


r»7.      5         3 


z-=:=pii 


^T^g^g^g^ 


Further  material  for  practice  is  afforded  by  all  chorales 
and  folk-songs,  the  former  given  as  soprano,  bass,  or 
inner  part. 


—     220     — 

Some  chorale-melodies  belong  to  the  old  Church  Modes, 
which  are  mentioned  in  the  ^^  Elem.  of  Harm.,"  §  116,  and  ex- 
haustively treated  of  in  ''strict  composition/'  For  the  present 
they  are  to  be  worked  out  with  modulations  ;  Dorian  and  ^olian 
as  7)iinor,  Ionian,  Lydian,  and  Mixolydian  as  7najor,  Phrygian  as 
mi?ior  from  dominant  to  dominant.  The  Phrygian  chorale 
"0  Haupt  voU  Blut  und  Wunden"  was  already  treated  by 
Bach  usually,  and  now  almost  exclusively,  as  a  major  melody 
beginning  and  closing  on  the  third. 

§  79. 

Exercise  54. 

We  now  give,  as  a  last  model  example,  a  perfect  master- 
work  of  harmonic  composition,  chosen  from  among  many  as 
best  adapted  for  this  purpose  on  account  of  its  pregnant  cha- 
racter within  small  compass.  The  pupil  should  analyze  it  in 
writing,  with  references  to  the  sections  of  this  hand-book. 

For  further  study  the  chorales  in  Bach's  "Passion  of  St. 
Matthew"  are  recommended. 


Soprano. 


Alto. 


Tenor.* 


Bass. 


Adagio. 


Ave  verum  corpus, 

by  Mozart. 


*  Elements  of  Harmony,  §  7. 


—    221    — 


^^- 


:^^E3E3E3 


ZZ»     *  J-6>-t:-'g 


\=± 


m 


na-tum    deMa-ri-a  vir 


gi  -  ne,      ve  -  re      pas  -  sum, 


^ 


3^=S 


-<9-*    -0- 


f^ 


^^^^^^^^^^^ 


r-t 


Pi 


f^3 


18 (2- 


1^^^^^ 


^^M 


S^ 


MIZ« 


^^^P§ 


mo  -  la  -  turn  in       cru    •     -    -    ce  pro    ho     -     mi- 


p^^^ 


^a^ 


'^^. 


m    cru    -   ce 


g 


W=^- 


«: 


iiS^^^i^ 


-&- 


is: 


:^t: 


im-mo    -    la  -  tum 


lE^^^j^^^>?^pf=]E^S^|^ 


ne;    cu-jus    la    -    tus  per  -   fo      -      ra    -    tum  un  -  da 


%- 


3^333; 


-&- 


3_;EE^E3E3Eg^ 


■^=X- 


CJ-     4- 


4^ n-> 


j^^j^^ 


^ 


m 


■•-=*■ 


P=^ 


1=4: 


ft^ 


t=i 


—     222     — 


^^ 


1 1- 


flu 


^^=:i=^ 


:^ 


P^9^^^3=S 


xit        et        san    -     -    gui  -  ne; 


i^i^~^ 


t=^: 


:t=±=t 


:^ 


1^ 


e  -  sto 


wm 


a 


(=-13: 


t-p'- 


^ 


-#-  -(S*'^ 


no  -  bis prae  -     -    -    gu  -  sta     -     turn  in  mor 


I 


^=3^ 


iziii 


•-J^fi*-- 


1=i: 


.__^_H 


iztzs: 


^ 


=^ 


HrM 


• — i<- 


sto  no 


bis- 


-prae 


^i 


^S=t 


t==t 


gu  -  sta  -  turn   in 


:-t 


^ 


B. 


3= 


=^-^— j^-i^ 


t=i: 


-6* 6»- 


— <9 ^— (g 1(9^ 


l=5t: 


-    -    tis      ex    -    a     «      mi  -   ne,     in      mor 


1=3 


S 


^ 


tz»: 


a    ^'  ^    -o 


m    mor 


Pi«-? 


tis 


->^ 


3 


223     — 


pa^-^tf^^F^I 


x=r. 


-S=isi 


Si 


:^3^ 


-12. 


Mozart  provided  this  composition  with  an  accompaniment 
by  string- quartet  and  organ,  which  also  carries  out  prelude, 
interlude,  and  postlude,  probably  merely  from  outward  con- 
sideration for  the  usages  of  Catholic  church-music  and  for  easier 
execution.  At  all  events,  this  work  has  been  long  familiar  in 
Germany  as  a  pure  vocal  composition.  Still,  the  omission  of 
the  accompaniment  has  occasioned  a  slight  alteration  in  the 
11*^  measure,  the  tenor  in  the  original  taking 


877. 


instead  of 


'%^ 


This  ^8  is  borrowed  from  Mozart's  instrumental  bass. 

With  the  words  "esto  nobis"  (at  A)  a  contrapuntal  (canonic) 
passage  begins,  which  consists  in  the  imitation  of  the  two 
higher  parts  by  the  two  lower  ones  in  a  different  interval  of 
the  key.  This  imitation  closes  with  the  first  note  of  the  5i^ 
measure  after  the  entrance  of  the  male  voices,  on  the  first 
syllable  of  the  word  "mortis"  (at  B). 

This  work,  from  the  last  years  of  Mozart*s  life,  shows 
what  complete  artistic  mastery,   paired  with  inspired  genius, 


—     224     — 

can  achieve  within  the  limits  of  a  very  short  and  compara- 
tively easily  executed  vocal  composition. 

After  thoroughly  working  out  the  foregoing  exercises,  the 
intending  student  of  composition  or  of  the  science  of  music 
will  be  prepared  to  begin  the  study  of  Counterpoint.  Thig 
latter  forms,  in  conjunction  with  the  course  in  Harmony,  the 
foundation  for  a  complete  and  sterling  technical  mastery  of  com- 
position. 


■p    m    ifl' 


Index. 

Figures  refer  to  page. 


Abbreviations    in    thorough  -  bass 

notation  214. 
Altered  chords  192,  208. 
Alto  17. 

Anticipations  94,  130,  137. 
Auftakt  (anacrusis,  initial  arsis)  127. 
Augmented  chord  of  the  sixth  198; 

triad  205. 
Ave  verum  corpus  (Mozart)  220. 

Bach  66,   108,   137,   182,  185,  214, 

215,  220. 
Bass  17. 

Beat,  strong  and  weak  24,  111,  128. 
Beethoven  66,  184,  193,  195,  212. 

Cadence  H  ;  five-chord  cadence  25 ; 

extended    cadence    67,     73—75; 

modulatory  -157. 
Chang  ing-dominant  1 75 — 1 77. 
Changing-notes  94, 132 ;  improperl07. 
Chorales,  Book  of  (Erk)  87. 
Chord-formation  40. 
Chords  in  general  3;  closing  33. 
Church  close  35;  modes  220. 
(7^■rc^e  of  fourths  and  fifths  147, 156. 
Close  14,  25;  different  styles  of  18, 

82;   partial  33;    full  34,  73,  82; 

modern  213;  with  organ-point  210.    | 
Bussler,  Elementary  Harmony. 


Close  harmony  6,  17;  position  16. 

Common  tones  6,  7,  10,  13,  19,  65, 
66,  147;  lack  of  11,  75. 

Compass  of  voices  17,  overstep- 
ped 157. 

Complex  passing-notes  105. 

Consonant  chords,  defined  29. 

Contrary  motion  13,  185;  wrong 
progression  prevented  by  14. 

Counterpoint  140,  182,  224. 

Covered  fifths  and  octaves  40. 

Cross-relation  148,  justifiable  150. 

Deceptive  close  174;  progressions  171 ; 
of  dominant  chord  173,  triad  174; 
of  subordinate  chord  of  the 
seventh  179;  of  augmented  chord 
of  sixth  202;  of  augmented 
triad  206. 

Diminished  chord  of  seventh  in 
modulating  161 ,  enharmonic 
character  of  166;  diminished  fifth 
after  perfect  48,  60;  diminished 
triad  49,  168,  on  11  in  minor  74. 

Dissonant  chord,  defined  30 ;  disso- 
nant principal  chords  29,  62 — 61 
in  modulation  147. 

Dominant  4;    chord  of  seventh  29, 


37;  triad  4. 


15 


226      — 


Double  suspension  135. 
Doubling  5,  21,  24,  30,  50,  100,  183, 
of  dissonant  intervals  97. 

Eleventh,  chord  of  the  126. 
Enharmonic  change    151,  161,  166, 

201,  206. 
Equal  temperament  214. 
Erk,  Book  of  Chorales  87. 

Fifths  and  fourths  in  melody  7. 

Flatted  second  192. 

Foreign  tones  94,  free  treatment  of 

133  ;  in  modulation  187. 
Four-part  chords  5. 
Fourth  and  sixth,  chord  of  23,  36  ; 

in  succession  72,  194. 
Free    leadings  52  ;    of  subordinate 

triads  78. 
Full  close  34,  73,  82. 
Fundamental  chord  29  ;  position  29, 

74  ;  triads  4,  interconnection  of  6. 

Half-close  34,  82,  194. 

Handel  66,  182. 

Harmonic  modulation  141  :  sequences 
153.-> 

Harmonizing  scale  9,  27,  35,  46,  75. 

Harmony,  close  and  open  16  ;  com- 
bined in  progression  18,  20. 

Hauptmann,'B.£ir\nomk.  u.  Metrik  26. 

Haydn  57,  66. 

Liner  parts,  6,  7,  8,  9,  17,  18,  19,  31, 
41,  45,  50,  55,  60,  61,  76,  100,  114, 
118. 

Intervals,  how  calculated  4. 

Inversion  21 — 23  ;  of  dominant  chord 
•  30,  chord  of  ninth  40,  minor  and 
diminished  chord  of  seventh  45, 
diminished  triad  50,  subordinate 
triads  71,  augmented  chord  of 
sixth  200. 

Key-note  in  modulation  142. 

Leading-note  30,  78  ;  in  suspensions 
113,  in  modulations  151. 


Liszt  184, 
Lotti  182. 


186.  212. 


Major  triad  4. 

Melody,    division    of,    into   sections 

33  ;  influence  on  harmony  34,  54, 

73,  80,  186—188. 
Mendelssohn  137,  182. 
Meyerbeer  136. 
Mixed  chords  192,  208. 
Mode,   change  of  142—144,  162  ;  in 

sequences  156. 
Modern  closes  213. 
Modulation  141  ;  to   adjacent   keys 

144  ;  diatonic,  chromatic,  and  en- 
harmonic 152. 
Modulatory  phrases  157. 
Motive  of  sequences  154,  177. 
Movement,  unbroken  119, 
Mozart    66,     173,     182,     186,    202, 

209,     212  ;     Ave    verum     corpus 

220. 

Neapolitan,  chord  of  sixth  193. 
Ninth,  chord  of  the  39  ;  maj&r  chord 

in   modulation   158,  minor  chord 

in  modulation  160. 

Oblique  motion  14. 

Omitted  tones     18,    20,    31,  32,    41, 

59. 
Open  harmony  17,  18,  20,  203. 
Opening  harmony  162, 
Organ-point  210. 

Parallel  fifths  10,  11,  39,  58,  with 
passing-notes  96,  with  suspen- 
sions 114  ;  fourths  82  ;  motion  10, 
18,  57,  in  all  parts  184  ;  octaves,  11, 
32,  58,  with  passing-notes  97,  with 
suspensions  114. 

Partiturstudium  213. 

Parts,  10,  the  four  (names,  compass, 
treatment),     17. 


—     227     — 


Passing-notes  94,  102,  105,  107,  137, 
on  weak  beats  96,  107, 

Perfect  fifth  after  diminislied  60. 

Permanent  modulation  141, 

Plagal  close  34. 

Position  of  higher  parts  7,  16 
(open  and  close);  in  relation  to 
bass  21. 

Principal  consonant  chords  3 ;  prin- 
cipal dissonant  chords  29. 

Progression  by  skips  and  steps  19. 

Rameau  2,  213. 
Related  chords  19. 
Resolution,  defined  30. 
Retarded  resolution  122. 

Scale,  harmonizing  the,  9,  27,  35,  46, 

75.^ 
Scarlatti  193. 
Schubert  208. 
Scoring,  Studies  in  213. 
Sequences,    harmonic    153;     with 

deceptive  progressions  177. 
Seventh,  dominant  chord  of  the  29, 

37;    minor   and  diminished  44; 

subordinate  chord  of,  on  11,  79 ; 

minor  chord  of,  in  modul.  159. 
Simple  passing-notes  94,  in  several 

pai-ts  102. 
Six- four  chord  23. 
Sixth,  chord  of  the  21,  in  succes- 
sion  22;    augmented    chord    of 

the  198. 
Sixth  and  fov/rth,  see  Fourth  and 

sixth. 
Skips,  progressions  by  15,  19,  22. 
Soprano  17. 
Steps,  progression  by  19. 


Suh-domi^ant  4;  triad  4;  substitutes 
for  in  modulation  168. 

Subordinate  chords  64;  triad  on  HI 
in  major  75;  subordinate  chord 
of  seventh  on  11,  79,  other 
ditto  181. 

Suspended  chords  126,  183. 

Suspensions  94,  107,  205,  tied  111; 
in  bass  117,  middle  parts  118; 
irregLilar  127;  two-part  121 ;  from 
below,  and  in  several  parts  124, 
209;  free  128;  free  treatment 
of  133. 

Syncopation  119. 

Temperament,  system  of  equal  214. 

Tenor  17. 

Ternary  time  95. 

Thirteenth,  chord  of  the  126. 

Thorough-bass  notation  88;  abbre- 
viations in  214. 

Tied  notes  112,  122. 

Tied  suspensions  111,  117,  without 
tie  127. 

Tonic  triad  3. 

Transposition  5. 

Transient  modulation  141. 

Triad,  tonic  3,  major  and  minor  4, 
dominant  and  sub-dominant  4, 
augmented  205;  progression  of 
triads  183. 

Triple  time  95,  105. 

Unison  between  two  parts  14. 

Vocal  chorus,  four-part  1. 
Voices,  compass  of  17,  overstepped 
157;  mutual  leading  of  14,  19. 

Wagner  173,  174,  202,  210. 
Well-tempered  Clavichord  214. 


15* 


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